Dissertations / Theses on the topic 'Patial Frequency Domain Imaging'

Le développent technologique des salles d’opérations a accéléré de manière spectaculaire ces dernières années. Cependant, la capacité des praticiens à différencier les tissus sains des tissus malsains à travers le champ chirurgical est principalement basée sur leur propre perception et expérience. Ceci est pourtant d’une importance majeure en chirurgie oncologique, tant pour la résection de tumeurs que pour les actes de reconstruction. C’est pourquoi la capacité d’évaluer le statut des tissus biologiques à travers des zones étendues en temps réel est cruciale. Le manque d’outils permettant l’évaluation de la viabilité des tissus biologique dans un contexte intra opératoire a été la motivation principale de ce projet. Un prototype d’imageur multimodal clinique a été développé pour l’imagerie d’oxygénation et de fluorescence en temps-réel. La capacité de la plateforme à quantifier l’ischémie a été démontrée lors de tests précliniques, par comparaison avec les méthodes standards. Le caractère multimodal de la plateforme d’imagerie a été exploité pour combiner l’imagerie endogène mesurant les propriétés optiques des tissus et l’imagerie exogène par fluorescence, dans le cadre de la chirurgie du cancer. Une méthode de quantification a été employée lors d’essais précliniques sur des modèles de cancers colorectaux et pancréatiques, mettant en évidence les défaillances de l’imagerie de fluorescence conventionnelle
The deployment of technology in operating rooms dramatically accelerated over the last decades. More precisely, the surgeons’ ability to distinguish healthy from diseased tissues is still mostly based on their own subjective perception. As tissue status assessment is of upmost importance in oncologic surgery, both for tumor resection and reconstruction procedures, the ability to assess the tissues intraoperatively and in real-time over a large field is crucial for surgical act guidance. The lack of tools for biological intraoperative tissue status assessment has been the main source of motivation for this thesis work. A clinically-compatible imaging platform has been developed for oxygenation and fluorescence imaging in real-time. The capability of the platform to detect and quantify ischemia has been demonstrated through preclinical trials, by comparison with standard of care methods. Furthermore, the multimodal nature of the developed imaging device has been exploited by combining endogenous imaging of optical properties with exogenous fluorescence imaging, in the context of oncologic surgery. A fluorescence quantification technique was validated in preclinical trials with colorectal and pancreatic cancer models, highlighting the limitations of conventional fluorescence imaging

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.
Includes bibliographical references (p. 81-87).
Optical coherence tomography (OCT) has emerged as a practical noninvasive technology for imaging the microstructure of the human eye in vivo. Using optical interferometry to spatially-resolve backreflections from within tissue, this high-resolution technique provides cross-sectional images of the anterior and posterior eye segments that had previously only been possible with histology. Current commercially-available OCT systems suffer limitations in speed and sensitivity, preventing them from effective screening of the retina and having a larger impact on the clinical environment. While other technological advances have addressed this problem, they are inadequate for imaging the choroid, which can be useful for evaluating choroidal disorders as well as early stages of retinal diseases. The objective of this thesis was to develop a new ophthalmic imaging method, termed optical frequency domain imaging (OFDI), to overcome these limitations. Preliminary imaging of the posterior segment of human eyes in vivo was performed to evaluate the utility of this instrument for comprehensive ophthalmic examination.
(cont.) The 1050-nm OFDI system developed for this thesis comprised a novel wavelength-swept laser that delivered 2.7 mW of average power at a sweep rate of 18.8 kHz, representing a two-order-of-magnitude improvement in speed over previously-demonstrated lasers in the 1050-nm range and below. The system, with an optical exposure level of 550 gW, achieved resolution of 10 gm in tissue and sensitivity of >92 dB over a depth range of 2.4 mm. Two healthy volunteers were imaged with the OFDI system, with 200,000 A-lines over 10.6 seconds in each imaging session. In comparison to results from a state-of-the-art spectral-domain OCT system, the OFDI system provided deeper penetration into the choroid. This thesis demonstrates OFDI's capability for comprehensive imaging of the human retina, optic disc, and choroid in vivo. The deep penetration power of the system enabled the first simultaneous visualization of retinal and choroidal vasculature without the exogenous dyes required by angiography. The combined capability for imaging microstructure and vasculature using a single instrument may be a significant factor influencing clinical acceptance of ophthalmic OFDI technology.
by Edward Chin Wang Lee.
S.M.

Thesis (Ph.D.)--Tufts University, 2004.
Adviser: Sergio Fantini. Submitted to the Dept. of Electrical Engineering. Includes bibliographical references (leaves 201-202). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Ground-penetrating radar (GPR) has the potential for high-resolution imaging of near-surface material properties, including electrical conductivity and permittivity, which can be used for geological interpretation of the near subsurface. This thesis presents ray-based traveltime inversion and frequency-domain full-waveform inversion (FWI) techniques for application to borehole GPR surveys. Ray-based traveltime inversion is attractive for its speed, reliability, and ability to work in 3D, but the ray approximation involved limits recoverable detail to greater than one wavelength. The traveltime method presented here uses an efficient and easily programmed fast-sweeping eikonal solver to compute traveltimes. The inversion method also incorporates the unknown time offset between signal transmission and start of recording at the receiver as a model parameter that is recovered simultaneously with the material slowness. The resolution of FWI approaches the diffraction limit of one half wavelength, but at a substantial computational cost. The FWI inversion scheme presented here works in 2D and is unique in its simultaneous recovery of the source wavelet, conductivity, and permittivity. Its frequency-domain formulation allows for efficient factorization of the forward modeling operator and its subsequent application to multiple right-hand sides in order to quickly construct the forward model Jacobian. Efficient calculation of the Jacobian allows the use of the Gauss-Newton technique rather than the gradient descent method that is common for other GPR FWI inversions. Measured data must be converted from 3D to 2D before use with this 2D FWI technique. I present a graphical derivation of the perpendicular ray Jacobian, which is an essential part of 3D to 2D transformation. The graphical derivation provides the reader with an intuitive understanding of the Jacobian that is difficult to obtain from traditional mathematical treatments. I also illustrate that 3D to 2D transfer functions previously derived for the acoustic case are applicable to borehole GPR.
Applied Science, Faculty of
Electrical and Computer Engineering, Department of
Graduate

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 26, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Ping Yu. Vita. Includes bibliographical references.

Fluorescence-enhanced optical imaging is an emerging non-invasive and non-ionizing modality towards breast cancer diagnosis. Various optical imaging systems are currently available, although most of them are limited by bulky instrumentation, or their inability to flexibly image different tissue volumes and shapes. Hand-held based optical imaging systems are a recent development for its improved portability, but are currently limited only to surface mapping. Herein, a novel optical imager, consisting primarily of a hand-held probe and a gain-modulated intensified charge coupled device (ICCD) detector, is developed towards both surface and tomographic breast imaging. The unique features of this hand-held probe based optical imager are its ability to; (i) image large tissue areas (5x10 sq. cm) in a single scan, (ii) reduce overall imaging time using a unique measurement geometry, and (iii) perform tomographic imaging for tumor three-dimensional (3-D) localization. Frequency-domain based experimental phantom studies have been performed on slab geometries (650 ml) under different target depths (1-2.5 cm), target volumes (0.45, 0.23 and 0.10 cc), fluorescence absorption contrast ratios (1:0, 1000:1 to 5:1), and number of targets (up to 3), using Indocyanine Green (ICG) as fluorescence contrast agents. An approximate extended Kalman filter based inverse algorithm has been adapted towards 3-D tomographic reconstructions. Single fluorescence target(s) was reconstructed when located: (i) upto 2.5 cm deep (at 1:0 contrast ratio) and 1.5 cm deep (upto 10:1 contrast ratio) for 0.45 cc-target; and (ii) 1.5 cm deep for target as small as 0.10 cc at 1:0 contrast ratio. In the case of multiple targets, two targets as close as 0.7 cm were tomographically resolved when located 1.5 cm deep. It was observed that performing multi-projection (here dual) based tomographic imaging using a priori target information from surface images. Improved the target depth recovery over using single projection based imaging. From a total of 98 experimental phantom studies, the sensitivity and specificity of the imager was estimated as 81-86% and 43-50%, respectively. With 3-D tomographic imaging successfully demonstrated for the first time using a hand-held based optical imager, the clinical translation of this technology is promising upon further experimental validation from in-vitro and in-vivo studies.

Le but de ce travail est de quantifier le potentiel et les capacités de la technologie térahertz à contrôler des colis afin de détecter les menaces telles que les armes et les explosifs, sans avoir besoin d'ouvrir le colis.Dans cette étude, nous présentons la spectroscopie térahertz résolue en temps et l'imagerie multi-spectrale pour la détection des explosifs. Deux types d’explosifs, ainsi que leurs mélanges binaires sont analysés. En raison de la complexité de l'extraction des informations face à tels échantillons, trois outils de chimiométrie sont utilisés: l’analyse en composantes principales (ACP), l'analyse des moindres carrés partiels (PLS) et l'analyse des moindres carrés partiels discriminante (PLS-DA). Les méthodes sont appliquées sur des données spectrales térahertz et sur des images spectrales pour : (i) décrire un ensemble de données inconnues et identifier des similitudes entre les échantillons par l'ACP ; (ii) créer des classes, ensuite classer les échantillons inconnus par PLS-DA ; (iii) créer un modèle capable de prédire les concentrations d’un explosif, à l'état pur ou dans des mélanges, par PLS.Dans la deuxième partie de ce travail, nous présentons l'imagerie par les ondes millimétriques pour la détection d'armes dans les colis. Trois techniques d'imagerie différentes sont étudiées : l'imagerie passive, l’imagerie active par des ondes continues (CW) et l’imagerie active par modulation de fréquence (FMCW). Les performances, les avantages et les limitations de chacune de ces techniques, pour l’inspection de colis, sont présentés. En outre, la technique de reconstruction tomographique est appliquée à chacune de ces trois techniques, pour visualiser en 3D et inspecter les colis en volume. Dans cet ordre, un algorithme de tomographie spécial est développé en prenant en considération la propagation gaussienne de l'onde
The aim of this work is to demonstrate the potential and capabilities of terahertz technology for parcels screening and inspection to detect threats such as weapons and explosives, without the need to open the parcel.In this study, we first present terahertz time-domain spectroscopy and spectral imaging for explosives detection. Two types of explosives as well as their binary mixture is analyzed. Due to the complexity of extracting information when facing such mixtures of samples, three chemometric tools are used: principal component analysis (PCA), partial least square analysis (PLS) and partial least squares-discriminant analysis (PLS-DA). The analyses are applied to terahertz spectral data and to spectral-images in order to: (i) describe a set of unknown data and identify similarities between samples by PCA; (ii) create a classification model and predict the belonging of unknown samples to each of the classes, by PLS-DA; (iii) create a model able to quantify and predict the explosive concentrations in a pure state or in mixtures, by PLS.The second part of this work focuses on millimeter wave imaging for weapon detection in parcels. Three different imaging techniques are studied: passive imaging, continuous wave (CW) active imaging and frequency modulated continuous wave (FMCW) active imaging. The performances, the advantages and the limitations of each of the three techniques, for parcel inspection, are exhibited. Moreover, computed tomography is applied to each of the three techniques to visualize data in 3D and inspect parcels in volume. Thus, a special tomography algorithm is developed by taking in consideration the Gaussian propagation of the wave

碩士
大葉大學
電機工程學系碩士班
91
In general, the RCS ( Radar Cross Section Area ) of target is measured by far field range to meet the quadratic phase error 22.5° ,i.e ,R≧4D^2/λ .For larger site of target the test range will be large. The compact range can provide larger site of quite for larger size of target RCS measurement. The radar image can be generated by ISAR (Inverse Synthetic Aperture Radar) techniques inside anechoic chamber with compact range. For the compact range with high performance, and larger site of quiet zone area, the cost is very high. In this paper, a low cost near field range will be used to measure the RCS of corner reflector and metal board. And the reason why the corner reflector and metal board have the same result in radar image. Besides, it can be measured in time domain by Impulse Time Domain System at Da-Yeh University. In fact, this system will replace the network vector analyzer in frequency domain. The Impulse Time Domain System can gate the reflection signal I want form the target. Because of the gating function, it can gate out the multipath and noise form environment. And the results of radar image from Frequency Domain and Tome Domain will be discussed. The characteristic of R-Card is applied to reduce the edge diffraction of reflection points. Besides, use R-Card to design a microwave absorber wall, and to reduce the multipath. The experimental precision will be promoted.

碩士
淡江大學
電機工程學系碩士班
101
This paper presents an inverse scattering problem for the through-wall imaging problem. Two separate perfect-conducting cylinders of unknown shapes are hidden behind a homogeneous building wall and illuminated by the transverse magnetic(TM) plane wave. After an integral formulation, a discretization using the method of moment (MoM) is applied. The through-wall imaging (TWI) problem is recast as a nonlinear optimization problem with an objective function defined by the norm of a difference between the measured and calculated scattered electric field. Thus, the shape of metallic cylinder can be obtained by minimizing the objective function. The Asynchronous particle swarm optimization is employed to find out the global extreme solution of the object function. Numerical results demonstrate even when the initial guesses are far away from the exact shapes, and then the multiple scattered fields between two conductors are serious the good reconstruction can be obtained. In addition, the effect of Gaussian noise on the reconstruction result is investigated and through the numerical simulation shows that we can still get good results of reconstructions.

Tissue optical properties, absorption, scattering and fluorescence, reveal important information about health, and holds the potential for non-invasive diagnosis and therefore earlier treatment for many diseases. On the other hand, tissue structure determines its function. Studying tissue structural properties helps us better understand structure-function relationship. Optical imaging is an ideal tool to study these tissue properties. However, conventional optical imaging techniques have limitations, such as not being able to quantitatively evaluate tissue absorption and scattering properties and only providing volumetrically averaged quantities with no depth control capability. To better study tissue properties, we integrated spatial frequency domain imaging (SFDI) with conventional reflectance imaging modalities. SFDI is a non-invasive, non-contact wide-field imaging technique which utilizes structured illumination to probe tissues. SFDI imaging is able to accurately quantify tissue optical properties. By adjusting spatial frequency, the imaging depth can be tuned which allows for depth controlled imaging. Especially at high spatial frequency, SFDI reflectance image is more sensitive to tissue scattering property than absorption property. The imaging capability of SFDI allows for studying tissue properties from a whole new perspective. In our study, we developed both benchtop and handheld SFDI imaging systems to accommodate different applications. By evaluating tissue optical properties, we corrected attenuation in fluorescence imaging using an analytical model; and we quantified optical and physical properties of skin diseases. By imaging at high spatial frequency, we demonstrated that absorption in fluorescence imaging can also be reduced because of a reduced imaging depth. This correction can be performed in real-time at 19 frames/second. Furthermore, fibrous structures orientation from the superficial layer can be accurately quantified in a multi-layered sample by limiting imaging depth. Finally, we color rendered SFDI reflectance image at high spatial frequency to reveal structural changes in skin lesions.

碩士
國立臺灣大學
生醫電子與資訊學研究所
102
Medical ultrasound imaging system is generally used as a diagnosis tool in clinical medicine. For general 2D imaging purpose, the system uses 1D array transducer to transmit/receive RF data, do the delay and sum beamforming (DAS), add some adequate imaging processing techniques, and finally, output the good quality image result in real-time. However, if 1D array transducer is replaced by 2D array for 3D imaging purpose, large RF data size will make the DAS too slow to keep the system real-time. Therefore, this research combines two techniques to speed up beamforming, that is, plane wave frequency domain beamforming (PWFDBF) and parallel programming on GPU. First, PWFDBF can use just one set of RF data to beamform one frame image. This feature will reduce the complexity and processing time of beamforming funamentally and enormously. Second, the powerful parallel processing ability of GPU will make PWFDBF ever faster. Field II is used in this research for creating simulated RF data. Then, Matlab is used for simulating PWFDBF and compounding imaging technique, verifying the correctness of the image result and doing the analytis of image quality. Finally, parallel programming PWFDBF is implemented on the PC with GPU by CUDA programming language. And Nsight is used for speed analysis. According to the experiment result, equivalent frame rate of PWFDBF can reach to the real-time standard(30 frames/s) under the simulated environment which is a 2D array transducer with 64 x 64 channels x 4096 samples. The result proves that the research is indeed a possible solution for 3D ultrasound imaging system according to the final processing time analysis result.

New methods to measure and quantify tissue molecular composition and metabolism are a major driver of discovery in basic and clinical research. Optical methods are well suited for this task based on the non-invasive nature of many imaging and spectroscopy techniques, the variety of exogenous fluorescent probes available, and the ability to utilize label-free endogenous absorption signatures of tissue chromophores including oxy- and deoxy-hemoglobin, water, lipid, collagen, and glucose. Despite significant advances in biomedical imaging, there remain challenges in probing tissue information in a fast, wide-field, and non-invasive manner. Moreover, quantitative in vivo mapping of endogenous biomarkers such as water and lipids remain relatively less explored by the biomedical optics community due to their characteristic extinction spectra, which have distinct spectral features in the shortwave infrared, a wavelength band that has been traditionally more challenging to measure. The work presented in this dissertation was focused on developing instrumentation and algorithms for non-invasive quantification of tissue optical properties, fluorophore concentrations, and chromophore concentrations in a wide-field imaging format. All of the imaging methods and algorithms developed in this thesis extend the capability of the emerging technique called Spatial Frequency Domain Imaging (SFDI). First, a new imaging technique based on SFDI is presented that can quantify the quantum yield of exogenous fluorophores in tissue. This technique can potentially provide a new non-invasive means for in vivo mapping of local tissue environment such as temperature and pH. Next, an angle correction algorithm was developed for SFDI for more accurate estimation of tissue optical properties as well as chromophore concentrations in highly curved tissue, including small animal tumor models. Next, a wide-field label-free optical imaging system was developed to simultaneously measure water and lipids using the shortwave infrared (SWIR) wavelength region. Last, to break the bottleneck of processing speed in optical property inversion, new deep learning based models were developed to provide over 300× processing speed improvement. Together, these projects substantially extend the available contrasts and throughput of SFDI, providing opportunities for new preclinical and clinical applications.
2020-10-22T00:00:00Z

The application of photoacoustic (PA) phenomena to medical imaging has been investigated for more than a decade. To implement this modality, one may choose between two types of laser sources, pulsed or continuous wave (CW). This selection affects all features of the imaging technique. Nowadays pulsed lasers are the state-of-the-art technique in the PA research. In this work, various features of the alternative frequency-domain (FD) PA were investigated. An axially symmetric transfer function model of PA wave generation and a Krimholtz-Leedom-Matthaei (KLM) transducer model were developed and used to analyze the experimental results. The controllable parameters of the FD-PA were optimized to improve the signal-to-noise ratio (SNR), contrast, axial resolution and depth detectivity. For example, it was shown that employing the optimal chirp bandwidth can enhance the SNR by more than 10 dB. In addition to the image produced by the cross-correlation amplitude, the phase of the correlation signal was used as a separate channel. A statistical method was introduced to generate an image from this phase channel, and also to filter the PA amplitude channel. A study was also performed to compare FD PA and the prevalent pulsed method. Various features of both methods were examined experimentally using a dual-mode PA system and under the condition of maximum permissible exposure (MPE). The SNRs of both methods were evaluated theoretically and experimentally. It was shown that at low frequencies, both modalities generate comparable SNRs, and at high frequencies pulsed PA produces superior SNRs and depth detetivity. However, by increasing the laser power and decreasing the chirp duration within the safety limits, the SNR and depth detectivity of the FD-PA method are enhanced considerably. The main cause to achieve lower experimental SNRs than theoretical predictions for pulsed PA response was shown to be the oscillating baseline, which can be partially eliminated by filtering.

abstract: Recent new experiments showed that wide-field imaging at millimeter scale is capable of recording hundreds of neurons in behaving mice brain. Monitoring hundreds of individual neurons at a high frame rate provides a promising tool for discovering spatiotemporal features of large neural networks. However, processing the massive data sets is impossible without automated procedures. Thus, this thesis aims at developing a new tool to automatically segment and track individual neuron cells. The new method used in this study employs two major ideas including feature extraction based on power spectral density of single neuron temporal activity and clustering tree to separate overlapping cells. To address issues associated with high-resolution imaging of a large recording area, focused areas and out-of-focus areas were analyzed separately. A static segmentation with a fixed PSD thresholding method is applied to within focus visual field. A dynamic segmentation by comparing maximum PSD with surrounding pixels is applied to out-of-focus area. Both approaches helped remove irrelevant pixels in the background. After detection of potential single cells, some of which appeared in groups due to overlapping cells in the image, a hierarchical clustering algorithm is applied to separate them. The hierarchical clustering uses correlation coefficient as a distance measurement to group similar pixels into single cells. As such, overlapping cells can be separated. We tested the entire algorithm using two real recordings with the respective truth carefully determined by manual inspections. The results show high accuracy on tested datasets while false positive error is controlled within an acceptable range. Furthermore, results indicate robustness of the algorithm when applied to different image sequences.
Dissertation/Thesis
Masters Thesis Electrical Engineering 2016

Despite significant advances in medical imaging technologies, there currently exist no tools to effectively assist healthcare professionals during surgical procedures. In turn, procedures remain subjective and dependent on experience, resulting in avoidable failure and significant quality of care disparities across hospitals. Optical techniques are gaining popularity in clinical research because they are low cost, non-invasive, portable, and can retrieve both fluorescence and endogenous contrast information, providing physiological information relative to perfusion, oxygenation, metabolism, hydration, and sub-cellular content. Near-infrared (NIR) light is especially well suited for biological tissue and does not cause tissue damage from ionizing radiation or heat. My dissertation has been focused on developing rapid imaging techniques for mapping endogenous tissue constituents to aid surgical guidance. These techniques allow, for the first time, video-rate quantitative acquisition over a large field of view (> 100 cm2) in widefield and endoscopic implementations. The optical system analysis has been focused on the spatial-frequency domain for its ease of quantitative measurements over large fields of view and for its recent development in real-time acquisition, single snapshot of optical properties (SSOP) imaging. Using these methods, this dissertation provides novel improvements and implementations to SSOP, including both widefield and endoscopic instrumentations capable of video-rate acquisition of optical properties and sample surface profile maps. In turn, these measures generate profile-corrected maps of hemoglobin concentration that are highly beneficial for perfusion and overall tissue viability. Also utilizing optical property maps, a novel technique for quantitative fluorescence imaging was also demonstrated, showing large improvement over standard and ratiometric methods. To enable real-time feedback, rapid processing algorithms were designed using lookup tables that provide a 100x improvement in processing speed. Finally, these techniques were demonstrated in vivo to investigate their ability for early detection of tissue failure due to ischemia. Both pre-clinical studies show endogenous contrast imaging can provide early measures of future tissue viability. The goal of this work has been to provide the foundation for real-time imaging systems that provide tissue constituent quantification for tissue viability assessments.
2018-01-09T00:00:00Z

The Shannon sampling framework is widely used for discrete representation of analog bandlimited signals, starting from samples taken at the Nyquist rate. In many practical applications, signals are not bandlimited. In order to accommodate such signals within the Shannon-Nyquist framework, one typically passes the signal through an anti-aliasing filter, which essentially performs bandlimiting. In applications such as RADAR, SONAR, ultrasound imaging, optical coherence to-mography, multiband signal communication, wideband spectrum sensing, etc., the signals to be sampled have a certain structure, which could manifest in one of the following forms: (i) sparsity or parsimony in a certain bases; (ii) shift-invariant representation; (iii) multi-band spectrum; (iv) finite rate of innovation property, etc.. By using such structure as a prior, one could devise efficient sampling strategies that operate at sub-Nyquist rates. In this Ph.D. thesis, we consider the problem of sampling and reconstruction of finite-rate-of-innovation (FRI) signals, which fall in one of the two classes: (i) Sum-of-weighted and time-shifted (SWTS) pulses; and (ii) Sum-of-weighted exponential (SWE). Finite-rate-of-innovation signals are not necessarily bandlimited, but they are specified by a finite number of free parameters per unit time interval. Hence, the FRI reconstruction problem could be solved by estimating the parameters starting from measurements on the signal. Typically, parameter estimation is done using high-resolution spectral estimation (HRSE) techniques such as the annihilating filter, matrix pencil method, estimation of signal parameter via rotational invariance technique (ESPRIT), etc.. The sampling issues include design of the sampling kernel and choice of the sampling grid structure. Following a frequency-domain reconstruction approach, we propose a novel technique to design compactly supported sampling kernels. The key idea is to cancel aliasing at certain set of uniformly spaced frequencies and make sure that the rest of the frequency response is specified such that the kernel follows the Paley-Wiener criterion for compactly supported functions. To assess the robustness in the presence of noise, we consider a particular class of the proposed kernel whose impulse response has the form of sum of modulated splines (SMS). In the presence of continuous-time and digital noise cases, we show that the reconstruction accuracy is improved by 5 to 25 dB by using the SMS kernel compared with the state-of-the-art compactly supported kernels. Apart from noise robustness, the SMS kernel also has polynomial-exponential reproducing property where the exponents are harmonically related. An interesting feature of the SMS kernel, in contrast with E-splines, is that its support is independent of the number of exponentials. In a typical SWTS signal reconstruction mechanism, first, the SWTS signal is trans formed to a SWE signal followed by uniform sampling, and then discrete-domain annihilation is applied for parameter estimation. In this thesis, we develop a continuous-time annihilation approach using the shift operator for estimating the parameters of SWE signals. Instead of using uniform sampling-based HRSE techniques, operator-based annihilation allows us to estimate parameters from structured non-uniform samples (SNS), and gives more accurate parameters estimates. On the application front, we first consider the problem of curve fitting and curve completion, specifically, ellipse fitting to uniform or non-uniform samples. In general, the ellipse fitting problem is solved by minimizing distance metrics such as the algebraic distance, geometric distance, etc.. It is known that when the samples are measured from an incomplete ellipse, such fitting techniques tend to estimate biased ellipse parameters and the estimated ellipses are relatively smaller than the ground truth. By taking into account the FRI property of an ellipse, we show how accurate ellipse fitting can be performed even to data measured from a partial ellipse. Our fitting technique first estimates the underlying sampling rate using annihilating filter and then carries out least-squares regression to estimate the ellipse parameters. The estimated ellipses have lesser bias compared with the state-of-the-art methods and the mean-squared error is lesser by about 2 to 10 dB. We show applications of ellipse fitting in iris images starting from partial edge contours. We found that the proposed method is able to localize iris/pupil more accurately compared with conventional methods. In a related application, we demonstrate curve completion to partial ellipses drawn on a touch-screen tablet. We also applied the FRI principle to imaging applications such as frequency-domain optical-coherence tomography (FDOCT) and nuclear magnetic resonance (NMR) spectroscopy. In these applications, the resolution is limited by the uncertainty principle, which, in turn, is limited by the number of measurements. By establishing the FRI property of the measurements, we show that one could attain super-resolved tomograms and NMR spectra by using the same or lesser number of samples compared with the classical Fourier-based techniques. In the case of FDOCT, by assuming a piecewise-constant refractive index of the specimen, we show that the measurements have SWE form. We show how super-resolved tomograms could be achieved using SNS-based reconstruction technique. To demonstrate clinical relevance, we consider FDOCT measurements obtained from the retinal pigment epithelium (RPE) and photoreceptor inner/outer segments (IS/OS) of the retina. We show that the proposed method is able to resolve the RPE and IS/OS layers by using only 40% of the available samples. In the context of NMR spectroscopy, the measured signal or free induction decay (FID) can be modelled as a SWE signal. Due to the exponential decay, the FIDs are non-stationary. Hence, one cannot directly apply autocorrelation-based methods such as ESPRIT. We develop DEESPRIT, a counterpart of ESPRIT for decaying exponentials. We consider FID measurements taken from amino acid mixture and show that the proposed method is able to resolve two closely spaced frequencies by using only 40% of the measurements. In summary, this thesis focuses on various aspects of sub-Nyquist sampling and demonstrates concrete applications to super-resolution imaging.

The Shannon sampling framework is widely used for discrete representation of analog bandlimited signals, starting from samples taken at the Nyquist rate. In many practical applications, signals are not bandlimited. In order to accommodate such signals within the Shannon-Nyquist framework, one typically passes the signal through an anti-aliasing filter, which essentially performs bandlimiting. In applications such as RADAR, SONAR, ultrasound imaging, optical coherence to-mography, multiband signal communication, wideband spectrum sensing, etc., the signals to be sampled have a certain structure, which could manifest in one of the following forms: (i) sparsity or parsimony in a certain bases; (ii) shift-invariant representation; (iii) multi-band spectrum; (iv) finite rate of innovation property, etc.. By using such structure as a prior, one could devise efficient sampling strategies that operate at sub-Nyquist rates. In this Ph.D. thesis, we consider the problem of sampling and reconstruction of finite-rate-of-innovation (FRI) signals, which fall in one of the two classes: (i) Sum-of-weighted and time-shifted (SWTS) pulses; and (ii) Sum-of-weighted exponential (SWE). Finite-rate-of-innovation signals are not necessarily bandlimited, but they are specified by a finite number of free parameters per unit time interval. Hence, the FRI reconstruction problem could be solved by estimating the parameters starting from measurements on the signal. Typically, parameter estimation is done using high-resolution spectral estimation (HRSE) techniques such as the annihilating filter, matrix pencil method, estimation of signal parameter via rotational invariance technique (ESPRIT), etc.. The sampling issues include design of the sampling kernel and choice of the sampling grid structure. Following a frequency-domain reconstruction approach, we propose a novel technique to design compactly supported sampling kernels. The key idea is to cancel aliasing at certain set of uniformly spaced frequencies and make sure that the rest of the frequency response is specified such that the kernel follows the Paley-Wiener criterion for compactly supported functions. To assess the robustness in the presence of noise, we consider a particular class of the proposed kernel whose impulse response has the form of sum of modulated splines (SMS). In the presence of continuous-time and digital noise cases, we show that the reconstruction accuracy is improved by 5 to 25 dB by using the SMS kernel compared with the state-of-the-art compactly supported kernels. Apart from noise robustness, the SMS kernel also has polynomial-exponential reproducing property where the exponents are harmonically related. An interesting feature of the SMS kernel, in contrast with E-splines, is that its support is independent of the number of exponentials. In a typical SWTS signal reconstruction mechanism, first, the SWTS signal is trans formed to a SWE signal followed by uniform sampling, and then discrete-domain annihilation is applied for parameter estimation. In this thesis, we develop a continuous-time annihilation approach using the shift operator for estimating the parameters of SWE signals. Instead of using uniform sampling-based HRSE techniques, operator-based annihilation allows us to estimate parameters from structured non-uniform samples (SNS), and gives more accurate parameters estimates. On the application front, we first consider the problem of curve fitting and curve completion, specifically, ellipse fitting to uniform or non-uniform samples. In general, the ellipse fitting problem is solved by minimizing distance metrics such as the algebraic distance, geometric distance, etc.. It is known that when the samples are measured from an incomplete ellipse, such fitting techniques tend to estimate biased ellipse parameters and the estimated ellipses are relatively smaller than the ground truth. By taking into account the FRI property of an ellipse, we show how accurate ellipse fitting can be performed even to data measured from a partial ellipse. Our fitting technique first estimates the underlying sampling rate using annihilating filter and then carries out least-squares regression to estimate the ellipse parameters. The estimated ellipses have lesser bias compared with the state-of-the-art methods and the mean-squared error is lesser by about 2 to 10 dB. We show applications of ellipse fitting in iris images starting from partial edge contours. We found that the proposed method is able to localize iris/pupil more accurately compared with conventional methods. In a related application, we demonstrate curve completion to partial ellipses drawn on a touch-screen tablet. We also applied the FRI principle to imaging applications such as frequency-domain optical-coherence tomography (FDOCT) and nuclear magnetic resonance (NMR) spectroscopy. In these applications, the resolution is limited by the uncertainty principle, which, in turn, is limited by the number of measurements. By establishing the FRI property of the measurements, we show that one could attain super-resolved tomograms and NMR spectra by using the same or lesser number of samples compared with the classical Fourier-based techniques. In the case of FDOCT, by assuming a piecewise-constant refractive index of the specimen, we show that the measurements have SWE form. We show how super-resolved tomograms could be achieved using SNS-based reconstruction technique. To demonstrate clinical relevance, we consider FDOCT measurements obtained from the retinal pigment epithelium (RPE) and photoreceptor inner/outer segments (IS/OS) of the retina. We show that the proposed method is able to resolve the RPE and IS/OS layers by using only 40% of the available samples. In the context of NMR spectroscopy, the measured signal or free induction decay (FID) can be modelled as a SWE signal. Due to the exponential decay, the FIDs are non-stationary. Hence, one cannot directly apply autocorrelation-based methods such as ESPRIT. We develop DEESPRIT, a counterpart of ESPRIT for decaying exponentials. We consider FID measurements taken from amino acid mixture and show that the proposed method is able to resolve two closely spaced frequencies by using only 40% of the measurements. In summary, this thesis focuses on various aspects of sub-Nyquist sampling and demonstrates concrete applications to super-resolution imaging.

This thesis presents the research results on the development of a microwave tomography imaging algorithm capable of reconstructing the dielectric properties of the unknown object. Our focus was on the theoretical aspects of the non-linear tomographic image reconstruction problem with particular emphasis on developing efficient numerical and non-linear optimization for solving the inverse scattering problem. A detailed description of a novel microwave tomography method based on frequency dependent finite difference time domain, a numerical method for solving Maxwell's equations and Genetic Algorithm (GA) as a global optimization technique is given. The proposed technique has the ability to deal with the heterogeneous and dispersive object with complex distribution of dielectric properties and to provide a quantitative image of permittivity and conductivity profile of the object. It is shown that the proposed technique is capable of using the multi-frequency, multi-view, and multi-incident planer techniques which provide useful information for the reconstruction of the dielectric properties profile and improve image quality. In addition, we show that when a-priori information about the object under test is known, it can be easily integrated with the inversion process. This provides realistic regularization of the solution and removes or reduces the possibility of non-true solutions. We further introduced application of the GA such as binary-coded GA, real-coded GA, hybrid binary and real coded GA, and neural-network/GA for solving the inverse scattering problem which improved the quality of the images as well as the conversion rate. The implications and possible advantages of each type of optimization are discussed, and synthetic inversion results are presented. The results showed that the proposed algorithm was capable of providing the quantitative images, although more research is still required to improve the image quality. In the proposed technique the computation time for solution convergence varies from a few hours to several days. Therefore, the parallel implementation of the algorithm was carried out to reduce the runtime. The proposed technique was evaluated for application in microwave breast cancer imaging as well as measurement data from university of Manitoba and Institut Frsenel's microwave tomography systems.

Η οπτική συνεκτική τομογραφία με τη χρήση συχνοτήτων ( FD-OCT) είναι μια ενδαγγειακή απεικονιστική μέθοδος που χρησιμοποιεί εγγύς στο υπέρυθρο φως, για να παράγει υψηλής ανάλυσης εικόνες του τοιχώματος του αυλού του αγγείου. Όπως και στην τεχνολογία υπερήχων, εκπέμπεται φωτεινή ενέργεια η οποία ανακλάται και εξασθενεί, σύμφωνα με την υφή του προσπιπτομένου ιστού. Το OCT μπορεί να απεικονίσει, με ανάλυση από 10 έως 20 μm, μικροδομές του αγγειακού τοιχώματος με εξαίσια λεπτομέρεια. Μέχρι σήμερα, η δυνατότητα εφαρμογής της μεθόδου είχε περιοριστεί σε μικρές αρτηρίες διαμέτρου έως 4mm και δεν είχε εφαρμοστεί in vivo στα αγγεία των κάτω άκρων, κάτωθεν του επιπέδου των βουβώνων. Σκοπός της παρούσας μελέτης είναι να αναφερθεί για παγκοσμίως πρώτη φορά η ασφάλεια και η σκοπιμότητα της απεικόνισης με Οπτική Συνεκτική Τομογραφία του αρτηριακού άξονα των κάτω άκρων , κάτωθεν του επιπέδου της βουβώνας ( μηροϊγνυακός άξονας και κνημιαία αγγεία), καθώς και οι σχετιζόμενες με το FD-OCT επιπλοκές. Επιπρόσθετα, να διερευνηθούν για πρώτη φορά, με τη χρήση FD-OCT, τα χαρακτηριστικά του αγγειακού τοιχώματος του ανωτέρω άξονα (τόσο πριν όσο και μετά από αγγειοπλαστική ή/και τοποθέτηση stent), η μορφολογία της αθηρωματικής πλάκας, η μορφολογία και η ποσοτικοποίηση της υπερπλασίας του νέου εσωτερικού χιτώνα (neointima) εντός του stent, η επαναστένωση εντός του stent (ISR) και η κακή εναπόθεση (malapposition) των stent struts σε μια σειρά από ασθενείς που πάσχουν από περιφερική αρτηριοπάθεια (PAD). Μελετήθηκαν, με ποσοτική ανάλυση του αυλού τους (Quantitative vascular analysis), αρτηρίες με διάμετρο έως 7 χιλιοστά. Μικτά χαρακτηριστικά από περιοχές πλούσιες σε λιπίδια, εναποθέσεις ασβεστίου και ασβεστοποιημένες πλάκες, νεκρωτικές περιοχές και ίνωση εντοπίστηκαν σε όλες τις απεικονιζόμενες αθηροσκληρωτικές βλάβες. Ωστόσο, με βάση το επικρατέστερο από τα παραπάνω απεικονιστικά χαρακτηριστικά, οι βλάβες στο πλαίσιο της έρευνας ταξινομήθηκαν ως αμιγώς ινωτικές, ως ινοασβεστοποιημένες, ως πλούσιες σε λιπίδια και τέλος ως νεκρωτικές/ασβεστοποιημένες. Συσσώρευση των μακροφάγων εντός της αθηρωματικής πλάκας σημειώθηκε σε μικρό ποσοστό των de novo αθηρωματικών αλλοιώσεων. Ποικίλοι βαθμοί υπερπλασίας του νέου έσω χιτώνα απεικονίσθηκαν σε όλες τις περιπτώσεις ISR αλλοιώσεων, με καθαρά ινωτικά χαρακτηριστικά και σημαντική νεοαγγείωση σε κάποιες από αυτές. Η νεοαγγείωση συνέπεσε με το επίπεδο της μέγιστης στένωσης του αγγειακού αυλού. Σημαντικού βαθμού διαχωρισμός με μεγάλο περιορισμό του αγγειακού αυλού, τέτοιος ώστε να απαιτηθεί να τοποθετηθεί ενδοαυλικό stent, ανιχνεύθηκε σε αρκετές περιπτώσεις της de novo αθηρωμάτωσης. Η ψηφιακή αφαιρετική αγγειογραφία παρέλειψε να προσδιορίσει μεγάλο ποσοστό των σοβαρών διαχωρισμών μετά από αγγειοπλαστική. Η νεοαθηροσκλήρυνση εντός του νέου έσω χιτώνα των κνημιαίων φαρμακευτικών stents (DES), είναι ένα συχνό εύρημα τόσο στους συμπτωματικούς όσο και στους ασυμπτωματικούς ασθενείς. Μπορούμε να υποθέσουμε ότι, κατά αναλογία με τα εμφυτευμένα DES στα στεφανιαία αγγεία, η ελαττωματική ενδοθηλιοποίηση που προκαλείται από την εκλυόμενη φαρμακευτική ουσία, μαζί με την νεοαγγείωση που αναπτύσσεται μεταξύ των stent struts, μπορούν να υποδαυλίσουν την νεοαθηροσκλήρυνση εντός του νέου έσω χιτώνα των κνημιαίων DES, η οποία μπορεί να οδηγήσει σε επαναστένωση εντός του stent (ISR) και απώλεια του εμβαδού του αυλού των περιφερικών αρτηριών. Οι παρατηρήσεις της μελέτης αυτής θέτουν σε αμφισβήτηση το παραδοσιακό τρόπο κατανόησης της περιφερειακής επαναστένωσης εντός του stent ως μιας απλής υπερπολλαπλασιαστικής απάντησης στο βαρότραυμα. Η απεικόνιση με FD-OCT είναι ένα βέλτιστο πειραματικό εργαλείο για την αξιολόγηση της εξέλιξης της αθηροσκληρωματικής νόσου και την επαναστένωση του αγγείου. Μπορεί να παρέχει υψηλής ευκρίνειας ενδοαγγειακή απεικόνιση κατά τη διάρκεια αγγειοπλαστικών επεμβάσεων στα κάτω άκρα και θα μπορούσε να αποδειχθεί κλινικά χρήσιμο για τον προσδιορισμό της εντός του stent πρόπτωσης ιστού και του strut malapposition. Παρ 'όλα αυτά, δεν πρέπει να χρησιμοποιηθεί ως εργαλείο για τη συνήθη κλινική πρακτική μέχρι να προκύψουν στοιχεία από περαιτέρω κλινικές δοκιμές για τον καθορισμό των ειδικών ενδείξεων της απεικόνισης με FD-OCT στις περιφερικές αρτηρίες.
Optical coherence tomography (OCT) is a catheter-based imaging method that employs near-infrared light to produce high-resolution intravascular images. OCT can readily visualize vessel microstructure at a 10- to 20-μm resolution with exquisite detail. To date, however, applicability of the method has been limited to small diameter arteries (≤4 mm). To the best of the author’s knowledge, this study is the first worldwide that demonstrates the safety and clinical feasibility of frequency domain Optical Coherence Tomography (FD-OCT) imaging of infrainguinal vessels in vivo during infrainguinal angioplasty procedures. It is also the first study that reports the use of intravascular FD-OCT to detect and characterize in-stent neointimal tissue following infrapopliteal drug eluting stent (DES) placement in patients suffering from critical limb ischemia. Quantitative lumen analysis of arteries with diameter up to 7 mm was performed. High-resolution OCT images provided exquisite two-dimensional axial and longitudinal views of the infrainguinal arteries and allowed thorough investigation of a variety of angioplasty sequela, including and not limited to intimal tears and dissection flaps, white and red thrombus, stent mesh malapposition, and intrastent plaque prolapse. Of interest, OCT identified cases of suboptimal postangioplasty outcome that single-plane subtraction angiography did not recognize and accounted. Mixed features of lipid pool areas, calcium deposits and calcified plaques, necrotic areas, and fibrosis were identified in all of the imaged atherosclerotic lesions. However, based on the predominant baseline imaging findings, lesions under investigation were classified as purely fibrotic, fibrocalcific, mostly lipid-laden and necrotic/calcified. Intraplaque accumulation of macrophages was noted in some of de novo atheromatic lesions. Varying degrees of neointimal hyperplasia were demonstrated in all cases of in stent restenosis (ISR) lesions with purely fibrotic features and considerable neovascularization in some of them. The latter finding coincided with the level of maximum vessel stenosis in all cases. Neoatherosclerosis following infrapopliteal DES placement is a frequent finding in both symptomatic and asymptomatic patients. Our preliminary observations allow us to speculate that analogous to coronary implanted DES, defective endothelialization induced by the eluted drug, along with neovascularization developing between the stent struts, may incite neointimal neoatherosclerosis, which may result in ISR and lumen loss of the peripheral arteries. It also seems that infrapopliteal neoatherosclerosis may be a significant contributing factor for ISR rather than a minor and sporadic process, highlighting the clinical significance of the phenomenon. Our observations put in dispute the traditional way of understanding peripheral in-stent restenosis as a simple hyperproliferative response to barotraumas and may explain the paramount importance of aggressive risk factor modification strategies. Neointimal neoatherosclerosis as identified by FD-OCT may have a role in the development of below-the-knee restenosis and thus warrants further investigation by larger controlled studies. Moreover, it may prove clinically useful for the determination of intrastent tissue prolapse and strut malapposition. FD-OCT should not be utilized as a tool for routine clinical practice until evidence from further clinical trials emerge to determine the specific indications for OCT imaging of the peripheral arteries.