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Journal articles on the topic 'Inverse Problems in Imaging'

Author: Grafiati
Published: 6 September 2023

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1

Ribes, Alejandro, and Francis Schmitt. "Linear inverse problems in imaging." IEEE Signal Processing Magazine 25, no. 4 (July 2008): 84–99. http://dx.doi.org/10.1109/msp.2008.923099.

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2

Gilton, Davis, Gregory Ongie, and Rebecca Willett. "Model Adaptation for Inverse Problems in Imaging." IEEE Transactions on Computational Imaging 7 (2021): 661–74. http://dx.doi.org/10.1109/tci.2021.3094714.

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3

Oksanen, Lauri, and Mikko Salo. "Inverse problems in imaging and engineering science." Mathematics in Engineering 2, no. 2 (2020): 287–89. http://dx.doi.org/10.3934/mine.2020014.

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4

Abubakar, Aria, and Maokun Li. "Electromagnetic Inverse Problems for Sensing and Imaging." IEEE Antennas and Propagation Magazine 58, no. 2 (April 2016): 17. http://dx.doi.org/10.1109/map.2016.2520879.

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5

Kravchuk, Oleg, and Galyna Kriukova. "Regularization by Denoising for Inverse Problems in Imaging." Mohyla Mathematical Journal 5 (December 28, 2022): 57–61. http://dx.doi.org/10.18523/2617-70805202257-61.

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In this work, a generalized scheme of regularization of inverse problems is considered, where a priori knowledge about the smoothness of the solution is given by means of some self-adjoint operator in the solution space. The formulation of the problem is considered, namely, in addition to the main inverse problem, an additional problem is defined, in which the solution is the right-hand side of the equation. Thus, for the regularization of the main inverse problem, an additional inverse problem is used, which brings information about the smoothness of the solution to the initial problem. This formulation of the problem makes it possible to use operators of high complexity for regularization of inverse problems, which is an urgent need in modern machine learning problems, in particular, in image processing problems. The paper examines the approximation error of the solution of the initial problem using an additional problem.
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6

Gilton, Davis, Gregory Ongie, and Rebecca Willett. "Deep Equilibrium Architectures for Inverse Problems in Imaging." IEEE Transactions on Computational Imaging 7 (2021): 1123–33. http://dx.doi.org/10.1109/tci.2021.3118944.

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7

Bryan, Kurt, and Tanya Leise. "Impedance Imaging, Inverse Problems, and Harry Potter's Cloak." SIAM Review 52, no. 2 (January 2010): 359–77. http://dx.doi.org/10.1137/090757873.

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8

Gilton, Davis, Greg Ongie, and Rebecca Willett. "Neumann Networks for Linear Inverse Problems in Imaging." IEEE Transactions on Computational Imaging 6 (2020): 328–43. http://dx.doi.org/10.1109/tci.2019.2948732.

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9

Ongie, Gregory, Ajil Jalal, Christopher A. Metzler, Richard G. Baraniuk, Alexandros G. Dimakis, and Rebecca Willett. "Deep Learning Techniques for Inverse Problems in Imaging." IEEE Journal on Selected Areas in Information Theory 1, no. 1 (May 2020): 39–56. http://dx.doi.org/10.1109/jsait.2020.2991563.

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10

Velikhovskyi, G. O., V. B. Molodkin, V. V. Lizunov, T. P. Vladimirova, S. V. Lizunova, Ya V. Vasylyk, M. P. Kulish, O. P. Dmytrenko, O. L. Pavlenko, and Iu V. Davydova. "Solving of Direct and Inverse Scattering Problems for Heterogeneous Non-Crystalline Objects in Analyzer-Based Imaging." METALLOFIZIKA I NOVEISHIE TEKHNOLOGII 41, no. 3 (May 26, 2019): 375–88. http://dx.doi.org/10.15407/mfint.41.03.0375.

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11

Habring, Andreas, and Martin Holler. "A Generative Variational Model for Inverse Problems in Imaging." SIAM Journal on Mathematics of Data Science 4, no. 1 (March 2022): 306–35. http://dx.doi.org/10.1137/21m1414978.

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12

Ebrahimi, M., and E. R. Vrscay. "Regularization schemes involving self-similarity in imaging inverse problems." Journal of Physics: Conference Series 124 (July 1, 2008): 012021. http://dx.doi.org/10.1088/1742-6596/124/1/012021.

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13

Lewis D., John, Vanika Singhal, and Angshul Majumdar. "Solving Inverse Problems in Imaging via Deep Dictionary Learning." IEEE Access 7 (2019): 37039–49. http://dx.doi.org/10.1109/access.2018.2881492.

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14

Jin, Kyong Hwan, Michael T. McCann, Emmanuel Froustey, and Michael Unser. "Deep Convolutional Neural Network for Inverse Problems in Imaging." IEEE Transactions on Image Processing 26, no. 9 (September 2017): 4509–22. http://dx.doi.org/10.1109/tip.2017.2713099.

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15

Szasz, Teodora, Adrian Basarab, and Denis Kouame. "Beamforming Through Regularized Inverse Problems in Ultrasound Medical Imaging." IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 63, no. 12 (December 2016): 2031–44. http://dx.doi.org/10.1109/tuffc.2016.2608939.

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16

Tang, Junqi, Karen Egiazarian, Mohammad Golbabaee, and Mike Davies. "The Practicality of Stochastic Optimization in Imaging Inverse Problems." IEEE Transactions on Computational Imaging 6 (2020): 1471–85. http://dx.doi.org/10.1109/tci.2020.3032101.

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17

Kaasalainen1, Mikko, and Josef Ďurech. "Inverse problems of NEO photometry: Imaging the NEO population." Proceedings of the International Astronomical Union 2, S236 (August 2006): 151–66. http://dx.doi.org/10.1017/s1743921307003195.

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AbstractThe physical properties of NEOs and other asteroids are mostly obtained with photometry. The resulting models describe the shapes, spin states, scattering properties and surface structure of the targets, and are the solutions of inverse problems involving comprehensive mathematical analysis. We review what can and cannot be obtained from photometric (and complementary) data, and how all this is done in practice. The role of photometry will become completely dominating with the advent of large-scale surveys capable of producing calibrated brightness data. Due to their quickly changing geometries with respect to the Earth, NEOs are the population that can be mapped the fastest.
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18

Rinkel, Jean, Jean Marie Polli, and Eduardo X. Miqueles. "X-ray coherent diffraction imaging: Sequential inverse problems simulation." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 912 (December 2018): 43–47. http://dx.doi.org/10.1016/j.nima.2017.10.032.

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19

Ren, Kui, Rongting Zhang, and Yimin Zhong. "Inverse transport problems in quantitative PAT for molecular imaging." Inverse Problems 31, no. 12 (November 30, 2015): 125012. http://dx.doi.org/10.1088/0266-5611/31/12/125012.

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20

Kwon, Kiwoon. "Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical Imaging." Advances in Mathematical Physics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/908251.

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Unique determination issues about inverse problems for elliptic partial differential equations in divergence form are summarized and discussed. The inverse problems include medical imaging problems including electrical impedance tomography (EIT), diffuse optical tomography (DOT), and inverse scattering problem (ISP) which is an elliptic inverse problem closely related with DOT and EIT. If the coefficient inside the divergence is isotropic, many uniqueness results are known. However, it is known that inverse problem with anisotropic coefficients has many possible coefficients giving the same measured data for the inverse problem. For anisotropic coefficient with anomaly with or without jumps from known or unknown background, nonuniqueness of the inverse problems is discussed and the relation to cloaking or illusion of the anomaly is explained. The uniqueness and nonuniqueness issues are discussed firstly for EIT and secondly for ISP in similar arguments. Arguing the relation between source-to-detector map and Dirichlet-to-Neumann map in DOT and the uniqueness and nonuniqueness of DOT are also explained.
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21

González-Rodríguez, Pedro, Arnold D. Kim, and Chrysoula Tsogka. "Corrigendum: Quantitative signal subspace imaging (2021 Inverse Problems 37 125006)." Inverse Problems 38, no. 4 (February 23, 2022): 049501. http://dx.doi.org/10.1088/1361-6420/ac509e.

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22

Tamburrino, A. "Monotonicity based imaging methods for elliptic and parabolic inverse problems." Journal of Inverse and Ill-posed Problems 14, no. 6 (September 2006): 633–42. http://dx.doi.org/10.1515/156939406778474578.

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23

Skinner, G. K., and T. J. Ponman. "Inverse problems in X-ray and gamma-ray astronomical imaging." Inverse Problems 11, no. 4 (August 1, 1995): 655–76. http://dx.doi.org/10.1088/0266-5611/11/4/004.

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24

Dave, Akshat, Anil Kumar Vadathya, Ramana Subramanyam, Rahul Baburajan, and Kaushik Mitra. "Solving Inverse Computational Imaging Problems Using Deep Pixel-Level Prior." IEEE Transactions on Computational Imaging 5, no. 1 (March 2019): 37–51. http://dx.doi.org/10.1109/tci.2018.2882698.

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25

Schirrmacher, Franziska, Christian Riess, and Thomas Kohler. "Adaptive Quantile Sparse Image (AQuaSI) Prior for Inverse Imaging Problems." IEEE Transactions on Computational Imaging 6 (2020): 503–17. http://dx.doi.org/10.1109/tci.2019.2956888.

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26

Raghavan, K. R., and A. E. Yagle. "Forward and inverse problems in elasticity imaging of soft tissues." IEEE Transactions on Nuclear Science 41, no. 4 (1994): 1639–48. http://dx.doi.org/10.1109/23.322961.

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27

McCann, Michael T., Kyong Hwan Jin, and Michael Unser. "Convolutional Neural Networks for Inverse Problems in Imaging: A Review." IEEE Signal Processing Magazine 34, no. 6 (November 2017): 85–95. http://dx.doi.org/10.1109/msp.2017.2739299.

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28

Raj, Raghu G. "A hierarchical Bayesian-MAP approach to inverse problems in imaging." Inverse Problems 32, no. 7 (May 12, 2016): 075003. http://dx.doi.org/10.1088/0266-5611/32/7/075003.

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29

Hosseini, Mahdi S., and Konstantinos N. Plataniotis. "Finite Differences in Forward and Inverse Imaging Problems: MaxPol Design." SIAM Journal on Imaging Sciences 10, no. 4 (January 2017): 1963–96. http://dx.doi.org/10.1137/17m1118452.

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30

Plessix, R. E. "A Helmholtz iterative solver for 3D seismic-imaging problems." GEOPHYSICS 72, no. 5 (September 2007): SM185—SM194. http://dx.doi.org/10.1190/1.2738849.

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A preconditioned iterative solver for the 3D frequency-domain wave equation applied to seismic problems is evaluated. The preconditioner corresponds to an approximate inverse of a heavily damped wave equation deduced from the (undamped) wave equation. The approximate inverse is computed with one multigrid cycle. Numerical results show that the method is robust and that the number of iterations increases roughly linearly with frequency when the grid spacing is adapted to keep a constant number of discretization points per wavelength. To evaluate the relevance of this iterative solver, the number of floating-point operations required for two imaging problems are roughly evaluated. This rough estimate indicates that the time-domain migration approach is more than one order of magnitude faster. The full-wave-form tomography, based on a least-squares formulation and a scale separation approach, has the same complexity in both domains.
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31

Guzzi, Francesco, Alessandra Gianoncelli, Fulvio Billè, Sergio Carrato, and George Kourousias. "Automatic Differentiation for Inverse Problems in X-ray Imaging and Microscopy." Life 13, no. 3 (February 23, 2023): 629. http://dx.doi.org/10.3390/life13030629.

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Computational techniques allow breaking the limits of traditional imaging methods, such as time restrictions, resolution, and optics flaws. While simple computational methods can be enough for highly controlled microscope setups or just for previews, an increased level of complexity is instead required for advanced setups, acquisition modalities or where uncertainty is high; the need for complex computational methods clashes with rapid design and execution. In all these cases, Automatic Differentiation, one of the subtopics of Artificial Intelligence, may offer a functional solution, but only if a GPU implementation is available. In this paper, we show how a framework built to solve just one optimisation problem can be employed for many different X-ray imaging inverse problems.
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32

Anjit, Thathamkulam Agamanan, Ria Benny, Philip Cherian, and Palayyan Mythili. "NON-ITERATIVE MICROWAVE IMAGING SOLUTIONS FOR INVERSE PROBLEMS USING DEEP LEARNING." Progress In Electromagnetics Research M 102 (2021): 53–63. http://dx.doi.org/10.2528/pierm21021304.

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33

Hyun, Chang Min, Seong Hyeon Baek, Mingyu Lee, Sung Min Lee, and Jin Keun Seo. "Deep learning-based solvability of underdetermined inverse problems in medical imaging." Medical Image Analysis 69 (April 2021): 101967. http://dx.doi.org/10.1016/j.media.2021.101967.

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34

Laves, Max-Heinrich, Malte Tölle, Alexander Schlaefer, and Sandy Engelhardt. "Posterior temperature optimized Bayesian models for inverse problems in medical imaging." Medical Image Analysis 78 (May 2022): 102382. http://dx.doi.org/10.1016/j.media.2022.102382.

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35

Lai, Ru-Yu, Kui Ren, and Ting Zhou. "Inverse Transport and Diffusion Problems in Photoacoustic Imaging with Nonlinear Absorption." SIAM Journal on Applied Mathematics 82, no. 2 (April 2022): 602–24. http://dx.doi.org/10.1137/21m1436178.

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36

Kim, Yong Y., and Rakesh K. Kapania. "Neural Networks for Inverse Problems in Damage Identification and Optical Imaging." AIAA Journal 41, no. 4 (April 2003): 732–40. http://dx.doi.org/10.2514/2.2004.

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37

Agarwal, Krishna, and Xudong Chen. "Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems." IEEE Transactions on Antennas and Propagation 56, no. 10 (October 2008): 3217–23. http://dx.doi.org/10.1109/tap.2008.929434.

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38

Oberai, Assad A., Nachiket H. Gokhale, and Gonzalo R. Feij o. "Solution of inverse problems in elasticity imaging using the adjoint method." Inverse Problems 19, no. 2 (February 6, 2003): 297–313. http://dx.doi.org/10.1088/0266-5611/19/2/304.

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39

Goutsias, John I., and Jerry M. Mendel. "Inverse problems in two‐dimensional acoustic media: A linear imaging model." Journal of the Acoustical Society of America 81, no. 5 (May 1987): 1471–85. http://dx.doi.org/10.1121/1.394500.

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40

Koo, Ja-Yong, and Peter T. Kim. "Sharp adaptation for spherical inverse problems with applications to medical imaging." Journal of Multivariate Analysis 99, no. 2 (February 2008): 165–90. http://dx.doi.org/10.1016/j.jmva.2006.06.007.

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41

Scales, J. A., P. Docherty, and A. Gersztenkorn. "Regularisation of nonlinear inverse problems: imaging the near-surface weathering layer." Inverse Problems 6, no. 1 (February 1, 1990): 115–31. http://dx.doi.org/10.1088/0266-5611/6/1/011.

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42

Anand, Christopher Kumar. "Robust Solvers for Inverse Imaging Problems Using Dense Single-Precision Hardware." Journal of Mathematical Imaging and Vision 33, no. 1 (August 28, 2008): 105–20. http://dx.doi.org/10.1007/s10851-008-0112-3.

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43

Chen, Zhiming, and Shiqi Zhou. "A direct imaging method for half-space inverse elastic scattering problems." Inverse Problems 35, no. 7 (June 25, 2019): 075004. http://dx.doi.org/10.1088/1361-6420/ab08ab.

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44

Repetti, Audrey, Marcelo Pereyra, and Yves Wiaux. "Scalable Bayesian Uncertainty Quantification in Imaging Inverse Problems via Convex Optimization." SIAM Journal on Imaging Sciences 12, no. 1 (January 2019): 87–118. http://dx.doi.org/10.1137/18m1173629.

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45

Kim, Taewoo, Renjie Zhou, Lynford L. Goddard, and Gabriel Popescu. "Solving inverse scattering problems in biological samples by quantitative phase imaging." Laser & Photonics Reviews 10, no. 1 (December 16, 2015): 13–39. http://dx.doi.org/10.1002/lpor.201400467.

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46

Evangelista, Davide, Elena Morotti, Elena Loli Piccolomini, and James Nagy. "Ambiguity in Solving Imaging Inverse Problems with Deep-Learning-Based Operators." Journal of Imaging 9, no. 7 (June 30, 2023): 133. http://dx.doi.org/10.3390/jimaging9070133.

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In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an ill-posed inverse problem and its solution is difficult to approximate when noise affects the data. Really, one limitation of neural networks for deblurring is their sensitivity to noise and other perturbations, which can lead to instability and produce poor reconstructions. In addition, networks do not necessarily take into account the numerical formulation of the underlying imaging problem when trained end-to-end. In this paper, we propose some strategies to improve stability without losing too much accuracy to deblur images with deep-learning-based methods. First, we suggest a very small neural architecture, which reduces the execution time for training, satisfying a green AI need, and does not extremely amplify noise in the computed image. Second, we introduce a unified framework where a pre-processing step balances the lack of stability of the following neural-network-based step. Two different pre-processors are presented. The former implements a strong parameter-free denoiser, and the latter is a variational-model-based regularized formulation of the latent imaging problem. This framework is also formally characterized by mathematical analysis. Numerical experiments are performed to verify the accuracy and stability of the proposed approaches for image deblurring when unknown or not-quantified noise is present; the results confirm that they improve the network stability with respect to noise. In particular, the model-based framework represents the most reliable trade-off between visual precision and robustness.
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47

Hou, Songming, Yihong Jiang, and Yuan Cheng. "Direct and Inverse Scattering Problems for Domains with Multiple Corners." International Journal of Partial Differential Equations 2015 (January 26, 2015): 1–9. http://dx.doi.org/10.1155/2015/968529.

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We proposed numerical methods for solving the direct and inverse scattering problems for domains with multiple corners. Both the near field and far field cases are considered. For the forward problem, the challenges of logarithmic singularity from Green’s functions and corner singularity are both taken care of. For the inverse problem, an efficient and robust direct imaging method is proposed. Multiple frequency data are combined to capture details while not losing robustness.
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48

Arridge, S., and A. Hauptmann. "Networks for Nonlinear Diffusion Problems in Imaging." Journal of Mathematical Imaging and Vision 62, no. 3 (September 13, 2019): 471–87. http://dx.doi.org/10.1007/s10851-019-00901-3.

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Abstract A multitude of imaging and vision tasks have seen recently a major transformation by deep learning methods and in particular by the application of convolutional neural networks. These methods achieve impressive results, even for applications where it is not apparent that convolutions are suited to capture the underlying physics. In this work, we develop a network architecture based on nonlinear diffusion processes, named DiffNet. By design, we obtain a nonlinear network architecture that is well suited for diffusion-related problems in imaging. Furthermore, the performed updates are explicit, by which we obtain better interpretability and generalisability compared to classical convolutional neural network architectures. The performance of DiffNet is tested on the inverse problem of nonlinear diffusion with the Perona–Malik filter on the STL-10 image dataset. We obtain competitive results to the established U-Net architecture, with a fraction of parameters and necessary training data.
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49

Denker, Alexander, Maximilian Schmidt, Johannes Leuschner, and Peter Maass. "Conditional Invertible Neural Networks for Medical Imaging." Journal of Imaging 7, no. 11 (November 17, 2021): 243. http://dx.doi.org/10.3390/jimaging7110243.

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Over recent years, deep learning methods have become an increasingly popular choice for solving tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point estimates for the reconstruction. However, especially in the analysis of ill-posed inverse problems, the study of uncertainties is essential. In our work, we apply generative flow-based models based on invertible neural networks to two challenging medical imaging tasks, i.e., low-dose computed tomography and accelerated medical resonance imaging. We test different architectures of invertible neural networks and provide extensive ablation studies. In most applications, a standard Gaussian is used as the base distribution for a flow-based model. Our results show that the choice of a radial distribution can improve the quality of reconstructions.
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50

Kaltenbacher, Barbara, and Kha Van Huynh. "Iterative regularization for constrained minimization formulations of nonlinear inverse problems." Computational Optimization and Applications 81, no. 2 (December 19, 2021): 569–611. http://dx.doi.org/10.1007/s10589-021-00343-x.

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AbstractIn this paper we study the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type methods. We carry out a convergence analysis in the sense of regularization methods and discuss applicability to the problem of identifying the spatially varying diffusivity in an elliptic PDE from different sets of observations. Among these is a novel hybrid imaging technology known as impedance acoustic tomography, for which we provide numerical experiments.
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