Journal articles: 'Compressive covariance estimation'

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Azizyan, Martin, Akshay Krishnamurthy, and Aarti Singh. "Extreme Compressive Sampling for Covariance Estimation." IEEE Transactions on Information Theory 64, no. 12 (December 2018): 7613–35. http://dx.doi.org/10.1109/tit.2018.2871077.

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Alwan, Nuha A. S. "Compressive Covariance Sensing-Based Power Spectrum Estimation of Real-Valued Signals Subject to Sub-Nyquist Sampling." Modelling and Simulation in Engineering 2021 (April 27, 2021): 1–9. http://dx.doi.org/10.1155/2021/5511486.

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In this work, an estimate of the power spectrum of a real-valued wide-sense stationary autoregressive signal is computed from sub-Nyquist or compressed measurements in additive white Gaussian noise. The problem is formulated using the concepts of compressive covariance sensing and Blackman-Tukey nonparametric spectrum estimation. Only the second-order statistics of the original signal, rather than the signal itself, need to be recovered from the compressed signal. This is achieved by solving the resulting overdetermined system of equations by application of least squares, thereby circumventing the need for applying the complicated ℓ 1 -minimization otherwise required for the reconstruction of the original signal. Moreover, the signal need not be spectrally sparse. A study of the performance of the power spectral estimator is conducted taking into account the properties of the different bases of the covariance subspace needed for compressive covariance sensing, as well as different linear sparse rulers by which compression is achieved. A method is proposed to benefit from the possible computational efficiency resulting from the use of the Fourier basis of the covariance subspace without considerably affecting the spectrum estimation performance.

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Pourkamali‐Anaraki, Farhad. "Estimation of the sample covariance matrix from compressive measurements." IET Signal Processing 10, no. 9 (December 2016): 1089–95. http://dx.doi.org/10.1049/iet-spr.2016.0169.

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Liu, Aihua, Qiang Yang, Xin Zhang, and Weibo Deng. "Direction-of-Arrival Estimation for Coprime Array Using Compressive Sensing Based Array Interpolation." International Journal of Antennas and Propagation 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/6425067.

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A method of direction-of-arrival (DOA) estimation using array interpolation is proposed in this paper to increase the number of resolvable sources and improve the DOA estimation performance for coprime array configuration with holes in its virtual array. The virtual symmetric nonuniform linear array (VSNLA) of coprime array signal model is introduced, with the conventional MUSIC with spatial smoothing algorithm (SS-MUSIC) applied on the continuous lags in the VSNLA; the degrees of freedom (DoFs) for DOA estimation are obviously not fully exploited. To effectively utilize the extent of DoFs offered by the coarray configuration, a compressing sensing based array interpolation algorithm is proposed. The compressing sensing technique is used to obtain the coarse initial DOA estimation, and a modified iterative initial DOA estimation based interpolation algorithm (IMCA-AI) is then utilized to obtain the final DOA estimation, which maps the sample covariance matrix of the VSNLA to the covariance matrix of a filled virtual symmetric uniform linear array (VSULA) with the same aperture size. The proposed DOA estimation method can efficiently improve the DOA estimation performance. The numerical simulations are provided to demonstrate the effectiveness of the proposed method.

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Prasanna, Dheeraj, and Chandra R. Murthy. "mmWave Channel Estimation via Compressive Covariance Estimation: Role of Sparsity and Intra-Vector Correlation." IEEE Transactions on Signal Processing 69 (2021): 2356–70. http://dx.doi.org/10.1109/tsp.2021.3070210.

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Monsalve, Jonathan, Juan Ramirez, Inaki Esnaola, and Henry Arguello. "Covariance Estimation From Compressive Data Partitions Using a Projected Gradient-Based Algorithm." IEEE Transactions on Image Processing 31 (2022): 4817–27. http://dx.doi.org/10.1109/tip.2022.3187285.

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Salari, Soheil, Francois Chan, Yiu-Tong Chan, Il-Min Kim, and Roger Cormier. "Joint DOA and Clutter Covariance Matrix Estimation in Compressive Sensing MIMO Radar." IEEE Transactions on Aerospace and Electronic Systems 55, no. 1 (February 2019): 318–31. http://dx.doi.org/10.1109/taes.2018.2850459.

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Li, Jian Feng, Xiao Fei Zhang, and Tong Hu. "Compressive Sensing-Based Angle Estimation for MIMO Radar with Multiple Snapshots." Applied Mechanics and Materials 347-350 (August 2013): 1028–32. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.1028.

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The issue of angle estimation for multiple-input multiple-output (MIMO) radar is studied and an algorithm for the estimation based on compressive sensing with multiple snapshots is proposed. The dimension of received signal is reduced to make the computation burden lower, and then the noise sensitivity is reduced by the eigenvalue decomposition (EVD) of the covariance matrix of the reduced-dimensional signal. Finally the signal subspace obtained from the eigenvectors is realigned to apply the orthogonal matching pursuit (OMP) for angle estimation. The angle estimation performance of the proposed algorithm is better than that of estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, and reduced-dimension Capon. Furthermore, the proposed algorithm works well for coherent targets, and requires no knowledge of the noise. The complexity analysis and simulation results verify the effectiveness of the algorithm.

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Wang, Ruisong, Gongliang Liu, Wenjing Kang, Bo Li, Ruofei Ma, and Chunsheng Zhu. "Bayesian Compressive Sensing Based Optimized Node Selection Scheme in Underwater Sensor Networks." Sensors 18, no. 8 (August 6, 2018): 2568. http://dx.doi.org/10.3390/s18082568.

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Information acquisition in underwater sensor networks is usually limited by energy and bandwidth. Fortunately, the received signal can be represented sparsely on some basis. Therefore, a compressed sensing method can be used to collect the information by selecting a subset of the total sensor nodes. The conventional compressed sensing scheme is to select some sensor nodes randomly. The network lifetime and the correlation of sensor nodes are not considered. Therefore, it is significant to adjust the sensor node selection scheme according to these factors for the superior performance. In this paper, an optimized sensor node selection scheme is given based on Bayesian estimation theory. The advantage of Bayesian estimation is to give the closed-form expression of posterior density function and error covariance matrix. The proposed optimization problem first aims at minimizing the mean square error (MSE) of Bayesian estimation based on a given error covariance matrix. Then, the non-convex optimization problem is transformed as a convex semidefinite programming problem by relaxing the constraints. Finally, the residual energy of each sensor node is taken into account as a constraint in the optimization problem. Simulation results demonstrate that the proposed scheme has better performance than a conventional compressed sensing scheme.

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Alwan, Nuha A. S., and Zahir M. Hussain. "Frequency Estimation from Compressed Measurements of a Sinusoid in Moving-Average Colored Noise." Electronics 10, no. 15 (July 31, 2021): 1852. http://dx.doi.org/10.3390/electronics10151852.

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Frequency estimation of a single sinusoid in colored noise has received a considerable amount of attention in the research community. Taking into account the recent emergence and advances in compressive covariance sensing (CCS), the aim of this work is to combine the two disciplines by studying the effects of compressed measurements of a single sinusoid in moving-average colored noise on its frequency estimation accuracy. CCS techniques can recover the second-order statistics of the original uncompressed signal from the compressed measurements, thereby enabling correlation-based frequency estimation of single tones in colored noise using higher order lags. Acceptable accuracy is achieved for moderate compression ratios and for a sufficiently large number of available compressed signal samples. It is expected that the proposed method would be advantageous in applications involving resource-limited systems such as wireless sensor networks.

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Paik, Ji Woong, Joon-Ho Lee, and Wooyoung Hong. "An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix." Sensors 21, no. 13 (June 27, 2021): 4403. http://dx.doi.org/10.3390/s21134403.

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An enhanced smoothed l0-norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed l0-norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.

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Zhang, Yahao, Yixin Yang, Long Yang, and Yong Wang. "Direction-of-arrival estimation for coherent signals through covariance-based grid free compressive sensing." JASA Express Letters 1, no. 9 (September 2021): 094801. http://dx.doi.org/10.1121/10.0006389.

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Park, Sungwoo, and Robert W. Heath. "Spatial Channel Covariance Estimation for the Hybrid MIMO Architecture: A Compressive Sensing-Based Approach." IEEE Transactions on Wireless Communications 17, no. 12 (December 2018): 8047–62. http://dx.doi.org/10.1109/twc.2018.2873592.

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Sahu, Smriti, and Neela Rayavarapu. "Compressive speech enhancement using semi-soft thresholding and improved threshold estimation." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 3 (June 1, 2023): 2788. http://dx.doi.org/10.11591/ijece.v13i3.pp2788-2800.

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<span lang="EN-US">Compressive speech enhancement is based on the compressive sensing (CS) sampling theory and utilizes the sparsity of the signal for its enhancement. To improve the performance of the discrete wavelet transform (DWT) basis-function based compressive speech enhancement algorithm, this study presents a semi-soft thresholding approach suggesting improved threshold estimation and threshold rescaling parameters. The semi-soft thresholding approach utilizes two thresholds, one threshold value is an improved universal threshold and the other is calculated based on the initial-silence-region of the signal. This study suggests that thresholding should be applied to both detail coefficients and approximation coefficients to remove noise effectively. The performances of the hard, soft, garrote and semi-soft thresholding approaches are compared based on objective quality and speech intelligibility measures. The normalized covariance measure is introduced as an effective intelligibility measure as it has a strong correlation with the intelligibility of the speech signal. A visual inspection of the output signal is used to verify the results. Experiments were conducted on the noisy speech corpus (NOIZEUS) speech database. The experimental results indicate that the proposed method of semi-soft thresholding using improved threshold estimation provides better enhancement compared to the other thresholding approaches.</span>

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Paik, Ji Woong, Wooyoung Hong, Jae-Kyun Ahn, and Joon-Ho Lee. "Statistics on noise covariance matrix for covariance fitting-based compressive sensing direction-of-arrival estimation algorithm: For use with optimization via regularization." Journal of the Acoustical Society of America 143, no. 6 (June 2018): 3883–90. http://dx.doi.org/10.1121/1.5042354.

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Yao, Di, Xin Zhang, Bin Hu, Qiang Yang, and Xiaochuan Wu. "Robust Adaptive Beamforming with Optimal Covariance Matrix Estimation in the Presence of Gain-Phase Errors." Sensors 20, no. 10 (May 21, 2020): 2930. http://dx.doi.org/10.3390/s20102930.

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An adaptive beamformer is sensitive to model mismatch, especially when the desired signal exists in the training samples. Focusing on the problem, this paper proposed a novel adaptive beamformer based on the interference-plus-noise covariance (INC) matrix reconstruction method, which is robust with gain-phase errors for uniform or sparse linear array. In this beamformer, the INC matrix is reconstructed by the estimated steering vector (SV) and the corresponding individual powers of the interference signals, as well as noise power. Firstly, a gain-phase errors model of the sensors is deduced based on the first-order Taylor series expansion. Secondly, sensor gain-phase errors, the directions of the interferences, and the desired signal can be accurately estimated by using an alternating descent method. Thirdly, the interferences and noise powers are estimated by solving a quadratic optimization problem. To reduce the computational complexity, we derive the closed-form solutions of the second and third steps with compressive sensing and total least squares methods. Simulation results and measured data demonstrate that the performance of the proposed beamformer is always close to the optimum, and outperforms other tested methods in the case of gain-phase errors.

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Hu, Ziying, Wei Wang, Fuwang Dong, and Ping Huang. "MIMO Radar Accurate 3-D Imaging and Motion Parameter Estimation for Target with Complex Motions." Sensors 19, no. 18 (September 13, 2019): 3961. http://dx.doi.org/10.3390/s19183961.

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In this paper, three-dimensional (3-D) multiple-input multiple-output (MIMO) radar accurate localization and imaging method with motion parameter estimation is proposed for targets with complex motions. To characterize the target accurately, a multi-dimensional signal model is established including the parameters on target 3-D position, translation velocity, and rotating angular velocity. For simplicity, the signal model is transformed into three-joint two-dimensional (2-D) parametric models by analyzing the motion characteristics. Then a gridless method based on atomic norm optimization is proposed to improve precision and simultaneously avoid basis mismatch in traditional compressive sensing (CS) techniques. Once the covariance matrix is obtained by solving the corresponding semi-definite program (SDP), estimating signal parameters via rotational invariance techniques (ESPRIT) can be used to estimate the positions, then motion parameters can be obtained by Least Square (LS) method, accordingly. Afterwards, pairing correction is carried out to remove registration errors by setting judgment conditions according to resolution performance analysis, to improve the accuracy. In this way, high-precision imaging can be realized without a spectral search process, and any slight changes of target posture can be detected accurately. Simulation results show that proposed method can realize accurate localization and imaging with motion parameter estimated efficiently.

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Peng, Li, Wang, Zhu, Liang, Fu, Du, Yang, and Xie. "SPICE-Based SAR Tomography Over Forest Areas Using a Small Number of P-band Airborne F-SAR Images Characterized by Non-Uniformly Distributed Baselines." Remote Sensing 11, no. 8 (April 23, 2019): 975. http://dx.doi.org/10.3390/rs11080975.

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Synthetic aperture radar tomography (TomoSAR) has been proven to be a useful way to reconstruct vertical structure over forest areas with P-band images, on account of its three-dimensional imaging ability. In the case of a small number of non-uniformly distributed acquisitions, compressive sensing (CS) is generally adopted in TomoSAR. However, the performance of CS depends on the selected hyperparameter, which is closely related to the noise of a pixel. In this paper, to overcome this limitation, we propose a sparse iterative covariance-based estimation (SPICE) approach based on the wavelet and orthogonal sparse basis (W&O-SPICE) for application over forest areas. SPICE is a sparse spectral estimation method that achieves a high vertical resolution, and takes account of the noise adaptively for each resolution cell. Thus, it does not require the user to select a hyperparameter. Furthermore, the used sparse basis not only ensures the sparsity of the forest canopy scattering contribution, but it can also keep the original sparse information of the ground contribution. The proposed method was tested in simulated experiments and the results demonstrated that W&O-SPICE can successfully reconstruct the vertical structure of a forest. Moreover, three P-band fully polarimetric airborne SAR images with non-uniformly distributed baselines were applied to reconstruct the vertical structure of a tropical forest in Mabounie, Gabon. The underlying topography and forest height were estimated, and the root-mean-square errors (RMSEs) were 6.40 m and 4.50 m with respect to the LiDAR digital terrain model (DTM) and canopy height model (CHM), respectively. In addition, W&O-SPICE showed a better performance than W&O-CS, beamforming, Capon, and the iterative adaptive approach (IAA).

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Martín-del-Campo-Becerra, Gustavo Daniel, Andreas Reigber, Matteo Nannini, and Scott Hensley. "Single-Look SAR Tomography of Urban Areas." Remote Sensing 12, no. 16 (August 8, 2020): 2555. http://dx.doi.org/10.3390/rs12162555.

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Synthetic aperture radar (SAR) tomography (TomoSAR) is a multibaseline interferometric technique that estimates the power spectrum pattern (PSP) along the perpendicular to the line-of-sight (PLOS) direction. TomoSAR achieves the separation of individual scatterers in layover areas, allowing for the 3D representation of urban zones. These scenes are typically characterized by buildings of different heights, with layover between the facades of the higher structures, the rooftop of the smaller edifices and the ground surface. Multilooking, as required by most spectral estimation techniques, reduces the azimuth-range spatial resolution, since it is accomplished through the averaging of adjacent values, e.g., via Boxcar filtering. Consequently, with the aim of avoiding the spatial mixture of sources due to multilooking, this article proposes a novel methodology to perform single-look TomoSAR over urban areas. First, a robust version of Capon is applied to focus the TomoSAR data, being robust against the rank-deficiencies of the data covariance matrices. Afterward, the recovered PSP is refined using statistical regularization, attaining resolution enhancement, suppression of artifacts and reduction of the ambiguity levels. The capabilities of the proposed methodology are demonstrated by means of strip-map airborne data of the Jet Propulsion Laboratory (JPL) and the National Aeronautics and Space Administration (NASA), acquired by the uninhabited aerial vehicle SAR (UAVSAR) system over the urban area of Munich, Germany in 2015. Making use of multipolarization data [horizontal/horizontal (HH), horizontal/vertical (HV) and vertical/vertical (VV)], a comparative analysis against popular focusing techniques for urban monitoring (i.e., matched filtering, Capon and compressive sensing (CS)) is addressed.

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Yuan, Sihan, and Daniel J. Eisenstein. "Decorrelating the errors of the galaxy correlation function with compact transformation matrices." Monthly Notices of the Royal Astronomical Society 486, no. 1 (March 27, 2019): 708–24. http://dx.doi.org/10.1093/mnras/stz899.

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Abstract Covariance matrix estimation is a persistent challenge for cosmology, often requiring a large number of synthetic mock catalogues. The off-diagonal components of the covariance matrix also make it difficult to show representative error bars on the 2-point correlation function (2PCF) since errors computed from the diagonal values of the covariance matrix greatly underestimate the uncertainties. We develop a routine for decorrelating the projected and anisotropic 2PCF with simple and scale-compact transformations on the 2PCF. These transformation matrices are modelled after the Cholesky decomposition and the symmetric square root of the Fisher matrix. Using mock catalogues, we show that the transformed projected and anisotropic 2PCF recover the same structure as the original 2PCF while producing largely decorrelated error bars. Specifically, we propose simple Cholesky-based transformation matrices that suppress the off-diagonal covariances on the projected 2PCF by ${\sim } 95{{\ \rm per\ cent}}$ and that on the anisotropic 2PCF by ${\sim } 87{{\ \rm per\ cent}}$. These transformations also serve as highly regularized models of the Fisher matrix, compressing the degrees of freedom so that one can fit for the Fisher matrix with a much smaller number of mocks.

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Ringh, Axel, Johan Karlsson, and Anders Lindquist. "Multidimensional Rational Covariance Extension with Applications to Spectral Estimation and Image Compression." SIAM Journal on Control and Optimization 54, no. 4 (January 2016): 1950–82. http://dx.doi.org/10.1137/15m1043236.

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Peyrega, Charles, Dominique Jeulin, Christine Delisée, and Jérôme Malvestio. "3D MORPHOLOGICAL MODELLING OF A RANDOM FIBROUS NETWORK." Image Analysis & Stereology 28, no. 3 (May 3, 2011): 129. http://dx.doi.org/10.5566/ias.v28.p129-141.

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In the framework of the Silent Wall ANR project, the CMM and the US2B are associated in order to characterize and to model fibrous media studying 3D images acquired with an X-Ray tomograph used by the US2B. The device can make 3D images of maximal 23043 voxels with resolutions in the range of 2 μm to 15 μm. Using mathematical morphology, measurements on the 3D X-Ray CT images are used to characterize materials. For example measuring the covariance on these images of an acoustic insulating material made of wooden fibres highlights the isotropy of the fibres orientations in the longitudinal planes which are perpendicular to the compression Oz axis. Moreover, it is possible to extract other morphological properties from these image processing methods such as the size distribution either of the fibres or of the pores by estimating the morphological opening granulometry of the considered medium. Using the theory of random sets introduced by Georges Matheron in the early 1970's, the aim of this work is to model such a fibrous material by parametric random media in 3D according to the prior knowledge of its morphological properties (covariance, porosity, size distributions, etc.). A Boolean model of random cylinders in 3D stacked in planes parallel to each other and perpendicular to the Oz compression axis is first considered. The granulometry results provide gamma distributions for the radii of the fibres. In addition, a uniform distribution of the orientations is chosen, according to the experimental isotropy measurements in the longitudinal planes. Finally the third statistical factor is the length distribution of the fibres which can be fitted by an exponential distribution. Thus it is possible to estimate the validity of this model first by trying to fit the experimental transverse and longitudinal covariances of the pores with the theoretical ones taking into account the statistical distributions of the dimensions of the random cylinders. The second method to validate the model consists in comparing morphological measurements (density profiles, covariance, opening granulometry, tortuosity, specific surface area) processed on real and on simulated media.

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Wang, Lanmei, Yao Wang, Guibao Wang, and Jianke Jia. "Near-field sound source localization using principal component analysis–multi-output support vector regression." International Journal of Distributed Sensor Networks 16, no. 4 (April 2020): 155014772091640. http://dx.doi.org/10.1177/1550147720916405.

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In this article, principal component analysis method, which is applied to image compression and feature extraction, is introduced into the dimension reduction of input characteristic variable of support vector regression, and a method of joint estimation of near-field angle and range based on principal component analysis dimension reduction is proposed. Signal-to-noise ratio and calculation amount are the decisive factors affecting the performance of the algorithm. Principal component analysis is used to fuse the main characteristics of training data and discard redundant information, the signal-to-noise ratio is improved, and the calculation amount is reduced accordingly. Similarly, support vector regression is used to model the signal, and the upper triangular elements of the signal covariance matrix are usually used as input features. Since the covariance matrix has more upper triangular elements, training it as a feature input will affect the training speed to some extent. Principal component analysis is used to reduce the dimensionality of the upper triangular element of the covariance matrix of the known signal, and it is used as the input feature of the multi-output support vector regression machine to construct the near-field parameter estimation model, and the parameter estimation of unknown signal is herein obtained. Simulation results show that this method has high estimation accuracy and training speed, and has strong adaptability at low signal-to-noise ratio, and the performance is better than that of the back-propagation neural network algorithm and the two-step multiple signal classification algorithm.

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Zeng, Huixian, and Jinguang Zeng. "Research on Black-Litterman Index Enhancement Strategy——Based on the Ledoit-Wolf Compression Estimation Method to Optimize the CSI 500 Index Enhancement Strategy." International Business Research 15, no. 2 (January 26, 2022): 60. http://dx.doi.org/10.5539/ibr.v15n2p60.

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Financial risks may often lead to significant losses. A reasonable capital management model can prevent financial risks and enhance financial services to the real economy. The Black-Litterman model can reduce risks through asset allocation. This paper uses the Black-Litterman model to construct an enhanced strategy applied to the CSI 500 Index, and selects the backtest from December 1, 2019 to December 1, 2021. Through the strategy backtest, it can be found that: whether it is considered or not Transaction costs, using analysts’ consensus target price as the input point of view of the BL model, can provide excess returns for the index enhancement strategy under relatively stable conditions within the sample interval, and improve the sharpness ratio, information ratio, maximum drawdown, etc. Within the risk-return parameters. In order to solve the problem of model instability and extreme values of configuration weights in the first step, this paper adjusts the covariance based on the Leodit-wolf compression estimation, thereby optimizing the exponential enhancement model. The backtest results showed that although the volatility and maximum drawdown of the optimized enhanced index model increased slightly, it showed a higher excess return rate and information ratio. Therefore, the BL model optimized based on the compression estimation method can make the model applicable to a wider range, and can be extended to large-scale assets and multi-asset allocation, so that investors have more choices in quantitative investment strategies.

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Dai, Shuxian, Yujin Zhang, Wanqing Song, Fei Wu, and Lijun Zhang. "Rotation Angle Estimation of JPEG Compressed Image by Cyclic Spectrum Analysis." Electronics 8, no. 12 (November 30, 2019): 1431. http://dx.doi.org/10.3390/electronics8121431.

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Image rotation is a common auxiliary method of image tampering, which can make the forged image more realistic from the geometric perspective. Most algorithms of image rotation angle estimation employ the peak value on the Fourier spectrum; however, JPEG post-processing brings additional peak interferences to the spectrum, which has a great impact on algorithm performance. In this paper, angle estimation is carried out for images compressed by JPEG. Firstly, the Fourier cyclic spectrum of image covariance is calculated, followed by semi-soft threshold wavelet transform to eliminate the block artefacts brought by JPEG compression. According to the shortest distance principle in the range of the limited amplitude, the processed cyclic spectral data are sorted to select the peak points. Finally, according to the selected peak point, the corresponding position coordinates of the theoretical peak point are found, and the rotation angle of the image is estimated by the theoretical peak point. Experimental results demonstrate that the average absolute error of the proposed algorithm is significantly lower than that of the state-of-the-art methods investigated, which highlights the promising potential of the proposed method as an image resampling detector in practical forensics applications.

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Ghalenoei, Emad, Jan Dettmer, Mohammed Y. Ali, and Jeong Woo Kim. "Trans-dimensional gravity and magnetic joint inversion for 3-D earth models." Geophysical Journal International 230, no. 1 (February 25, 2022): 363–76. http://dx.doi.org/10.1093/gji/ggac083.

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SUMMARY Studying 3-D subsurface structure based on spatial data is an important application for geophysical inversions. However, major limitations exist for conventional regularized inversion when applied to potential-field data. For example, global regularization parameters can mask model features that may be important for interpretation. In addition, 3-D inversions are typically based on data acquired in 2-D at the Earth’s surface. Such data may contain significant spatial error correlations in 2-D due to the choice of spatial sampling, acquisition geometry, ambient noise and model assumptions. These correlations can cause trade-offs with spatial resolution and should be accounted for. However, correlations are often ignored, particularly 2-D correlations in spatial data, such as potential field data recorded on the Earth’s surface. Non-linear Bayesian methods can address these shortcomings and we present a new hierarchical model for 2-D correlated errors. Nonetheless, limitations also exist. For example, non-linear Bayesian estimation requires numerical integration with a considerable computational burden to collect a posterior ensemble of models. For 3-D applications, this cost can be prohibitive. This paper presents a non-linear Bayesian inversion with trans-dimensional (trans-D) partitioning of space by a hierarchy of Voronoi nodes and planes (VP), and trans-D estimation of the data noise covariance matrix. The addition of planes permits the introduction of prior information which reduces non-uniqueness. The covariance matrix estimation uses a trans-D autoregressive (AR) noise model to quantify correlated noise on 2-D potential-field data. We address computational cost by wavelet compression in the forward problem and by basing susceptibility on an empirical relationship with density contrast. The method is applied to simulated data and field data from off-shore Abu Dhabi. With simulated data, we demonstrate that subsurface structures are well-resolved with the trans-D model that applies hierarchical VP partitioning. In addition, the model locally adapts based on data information without requiring regularization. The method is also successful in reducing 2-D error correlation via trans-D AR models in 2-D. From field data, the inversion efficiently resolves basement topography and two distinct salt diapirs with a parsimonious and data-driven parametrization. Results show a considerable reduction in 2-D spatial correlations of field data using the proposed trans-D AR model.

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Parbhoo, Sonali, Mario Wieser, Aleksander Wieczorek, and Volker Roth. "Information Bottleneck for Estimating Treatment Effects with Systematically Missing Covariates." Entropy 22, no. 4 (March 29, 2020): 389. http://dx.doi.org/10.3390/e22040389.

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Estimating the effects of an intervention from high-dimensional observational data is a challenging problem due to the existence of confounding. The task is often further complicated in healthcare applications where a set of observations may be entirely missing for certain patients at test time, thereby prohibiting accurate inference. In this paper, we address this issue using an approach based on the information bottleneck to reason about the effects of interventions. To this end, we first train an information bottleneck to perform a low-dimensional compression of covariates by explicitly considering the relevance of information for treatment effects. As a second step, we subsequently use the compressed covariates to perform a transfer of relevant information to cases where data are missing during testing. In doing so, we can reliably and accurately estimate treatment effects even in the absence of a full set of covariate information at test time. Our results on two causal inference benchmarks and a real application for treating sepsis show that our method achieves state-of-the-art performance, without compromising interpretability.

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Tompkins, Michael J., Juan L. Fernández Martínez, David L. Alumbaugh, and Tapan Mukerji. "Scalable uncertainty estimation for nonlinear inverse problems using parameter reduction, constraint mapping, and geometric sampling: Marine controlled-source electromagnetic examples." GEOPHYSICS 76, no. 4 (July 2011): F263—F281. http://dx.doi.org/10.1190/1.3581355.

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We have developed a new uncertainty estimation method that accounts for nonlinearity inherent in most geophysical problems, allows for the explicit search of model posterior space, is scalable, and maintains computational efficiencies on the order of deterministic inverse solutions. We accomplish this by combining an efficient parameter reduction technique, a parameter constraint mapping routine, a sparse geometric sampling scheme, and an efficient forward solver. In order to reduce our model domain and determine an independent basis, we implement both a typical principal component analysis, which factorizes the model covariance matrix, and an alternative compression method, based on singular-value decomposition, which acts on training models, directly, and is storage efficient. Once we have a reduced base, we map parameter constraints, from our original model domain, to this reduced domain to define a bounded geometric region of feasible model space. We utilize an optimal scheme to sample this reduced model space that uses Smolyak sparse grids and minimizes the number of forward solves by finding the sparsest sampling required to produce convergent uncertainty measures. The result is an ensemble of equivalent models, consistent with our inverse solution structure, which is used to infer inverse uncertainty. We tested our method with a 1D synthetic example, a comparison with a published Metropolis-Hastings sampling example, and an extension to 2D problems using a field data inversion.

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Angielczyk, Kenneth D., and H. David Sheets. "Investigation of simulated tectonic deformation in fossils using geometric morphometrics." Paleobiology 33, no. 1 (2007): 125–48. http://dx.doi.org/10.1666/06007.1.

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Abstract:

Tectonic deformation is an important part of the taphonomic histories of many fossils. Although the effects of deformation, and methods to remove those effects, have been a subject of inquiry for over a century, systematic testing under known parameters has never been used to determine how the effects of deformation and the performance of retrodeformation techniques might vary. Comparative studies of morphology depend on the accurate estimation of variance-covariance structure, so an understanding of the effects of retrodeformation on covariance structure is important in assessing the utility of these methods. Here we address these issues by using geometric morphometric simulations. Nondeformed data sets were generated from specimens of the extant turtle Emys marmorata, which were known by definition to be nondeformed, and which possess a known ontogenetic signal. Deformation was simulated by applying a combination of uniform shear and uniform compression/dilation to the data. Data were retrodeformed by reflection and averaging of bilaterally symmetric landmarks, use of a principal components analysis to identify a deformation component of shape variation, and removal of the affine component of shape variation among specimens. Deformation increased the amount of variance in the data, as well as altering the variance structure. However, low to moderate levels of deformation did not prevent the confident recovery of the known ontogenetic signal in some cases. The tested retrodeformation techniques did not work well. They either removed too little or too much variance from the data, and provided little improvement in variance structure. Retrodeformation often did not improve our ability to extract the ontogenetic signal from the data, and in some cases introduced an arti-factual relationship between size and shape. All of the scrutinized methods showed some properties, such as reducing variance or producing visually appealing images of specimens, that could make them appear to be working in cases where the correct biological signal is not known. This emphasizes the need for simulation testing in the development and evaluation of retrodeformation techniques.

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"On-grid Adaptive Compressive Sensing Framework for Underdetermined DOA Estimation by Employing Singular Value Decomposition." International Journal of Innovative Technology and Exploring Engineering 8, no. 11 (September 10, 2019): 3076–82. http://dx.doi.org/10.35940/ijitee.k2433.0981119.

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Abstract:

In the field of Array Signal Processing, the problem of Direction of Arrival (DOA) estimation has attracted colossal attention of researchers in the past few years. The problem refers to estimating the angle of arrival of the incoming signals at the receiver end, from the knowledge of the received signal itself. Generally, an array of antenna/sensors is employed at the receiver for this purpose. In over-determined DOA estimation, the number of signal sources, whose direction needs to be estimated are usually lesser than half the number of antenna array elements, whereas the challenge is to estimate the DOAs in under-determined case, where the signal source number is quiet larger than the number of antenna array elements. This paper tackles such a problem by the application of multiple level nested array. Instead of subspace-based techniques for the estimation, sparse signal representation for Compressive Sensing (CS) framework is used, which eliminates the requirement of prior information about the source number and also the tedious task of computing the inverse of the covariance matrices. In this paper, we propose an adaptive approach for Least Absolute Shrinkage and Selection Operator (LASSO) with reduced number of computations by singular value decomposing of the received signal vector. The outcomes of this paper showcase that the presented algorithm achieves high degree of freedom (DOF), good resolution, minimum root mean square error and less computational complexity with increased speed of estimation.

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Journal articles on the topic 'Compressive covariance estimation'

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