Low-rank Matrix Recovery Method Research Articles

Parameter Optimization for Low-Rank Matrix Recovery in Hyperspectral Imaging

An approach to parameter optimization for the low-rank matrix recovery method in hyperspectral imaging is discussed. We formulate an optimization problem with respect to the initial parameters of the low-rank matrix recovery method. The performance for different parameter settings is compared in terms of computational times and memory. The results are evaluated by computing the peak signal-to-noise ratio as a quantitative measure. The potential improvement in the performance of the noise reduction method is discussed when optimizing the choice of the initial values. The optimization method is tested on standard and openly available hyperspectral data sets, including Indian Pines, Pavia Centre, and Pavia University.

Highly undersampling dynamic cardiac MRI based on low-rank tensor coding

Dynamic cardiac magnetic resonance imaging (CMRI) is an important tool for the non-invasive assessment of cardiovascular disease. However, dynamic CMRI suffers from long acquisition times due to the need of obtaining images with high temporal and spatial resolution, whole-heart coverage. Conventionally, a multidimensional dataset in dynamic CMRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the sparsity of MR images. In this paper, we propose a low-rank tensor coding (LRTC) model with tensor sparsity for the application of compressive sensing (CS) in dynamic CMRI. In this framework, each group of 3D similar patches extracted from high-dimensional images is considered to be a low-rank tensor. LRTC can better capture the sparse part of dynamic CMRI and make full use of the redundancy between the feature vectors of adjacent positions. ADMM technique is introduced to tackle the proposed model, where soft threshold operator is used to solving the l1 norm relaxation. Higher-order singular value decomposition (HOSVD) is exploited to process high-dimensional tensors and mine correlations in space-time dimensions. Validations based on cardiac cine and myocardial perfusion datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods, and outperformed the conventional sparse recovery methods.

Fast Construction of the Radio Map Based on the Improved Low-Rank Matrix Completion and Recovery Method for an Indoor Positioning System

With the development of information technology, indoor positioning technology has been rapidly evolving. Due to the advantages of high positioning accuracy, low cost, and wide coverage simultaneously, received signal strength- (RSS-) based WLAN indoor positioning technology has become one of the mainstream technologies. A radio map is the basis for the realization of the WLAN positioning system. However, by reasons of the huge workload of RSS collection, the instability of wireless signal strength, and the disappearance of signals caused by the occlusion of people and objects, the construction of a radio map is time-consuming and inefficient. In order to rapidly deploy the WLAN indoor positioning system, an improved low-rank matrix completion method is proposed to construct the radio map. Firstly, we evenly arrange a small number of reference points (RP) in the positioning area and collect RSS data on the RP to construct the radio map. Then, the low-rank matrix completion method is used to fill a small amount of data in the radio map into a complete database. The Frobenius parameter (F-parameter) is introduced into the traditional low-rank matrix completion model to control the instability of the model solution when filling the data. To solve the noise problem caused by environment and equipment, a low-rank matrix recovery algorithm is used to eliminate noise. The experimental results show that the improved algorithm achieves the expected goal.

Rank-1 Matrix Approximation-Based Channel Estimation for Intelligent Reflecting Surface-Aided Multi-User MISO Communications

The acquisition of channel state information is an essential step in enabling intelligent reflecting surfaces (IRSs) for wireless communications. In this letter, we introduce a novel procedure to estimate the cascaded channel between the base station (BS), IRS, and users in a multi-user multiple-input single-output system. The common BS-IRS channel, over which all users transmit, is leveraged to decompose the cascaded channel into a series of rank-1 matrices. Low-rank matrix recovery methods are utilized to improve upon the linear minimum mean-squared error estimate of the cascaded channel. A theoretical upper bound for the mean-square error (MSE) of the proposed estimator is derived. Numerical results reveal that the proposed techniques outperform the existing counterparts in terms of the MSE and scale with the number of BS antennas.

Wind data extrapolation and stochastic field statistics estimation via compressive sampling and low rank matrix recovery methods

A methodology based on compressive sampling is developed for incomplete wind time-histories reconstruction and extrapolation in a single spatial dimension, as well as for related stochastic field statistics estimation. This relies on l1-norm minimization in conjunction with an adaptive basis re-weighting scheme. Indicatively, the proposed methodology can be employed for monitoring of wind turbine systems, where the objective relates to either reconstructing incomplete time-histories measured at specific points along the height of a turbine tower, or to extrapolating to other locations in the vertical dimension where sensors and measurement records are not available. Further, the methodology can be used potentially for environmental hazard modeling within the context of performance-based design optimization of structural systems. Unfortunately, a straightforward implementation of the aforementioned approach to account for two spatial dimensions is hindered by significant, even prohibitive in some cases, computational cost. In this regard, to address computational challenges associated with higher-dimensional domains, a methodology based on low rank matrices and nuclear norm minimization is developed next for wind field extrapolation in two spatial dimensions. The efficacy of the proposed methodologies is demonstrated by considering various numerical examples. These refer to reconstruction of wind time-histories with missing data compatible with a joint wavenumber-frequency power spectral density, as well as to extrapolation to various locations in the spatial domain.

New Suppression Technology for Low-Frequency Noise in Desert Region: The Improved Robust Principal Component Analysis Based on Prediction of Neural Network

Lots of low-frequency noise including random noise and surface waves seriously reduces the quality of desert seismic data. However, the suppression for desert low-frequency noise faces three main problems: nonstationary and non-Gaussian of random noise; strong energy of low-frequency noise; a more serious frequency-band overlap between effective signals and low-frequency noise. Robust principal component analysis (RPCA) is a classical low-rank matrix (LM) recovery method which is very suitable for processing nonlinear noise. It can decompose noisy data to the optimal LM and sparse matrix (SM), which include most effective signals and noise, respectively. Therefore, the RPCA is introduced to suppress desert low-frequency noise. However, due to the low signal-to-noise ratio (SNR) and serious frequency-band overlap, much low-frequency noise still remains in the LM of desert seismic data after the decomposition of RPCA. Meanwhile, some nonnegligible effective signals are decomposed into the SM of desert seismic data. To solve this problem, the convolutional neural network (CNN) is introduced to extract effective signals from SM and LM. By constructing suitable training sets to guide the CNN's training, the CNN denoising models after training are used to predict the effective signals from these two matrices, respectively. In this article, to approach real desert seismic data, we use a variety of seismic wavelets to simulate different types of seismic events, and then use these synthetic seismic events and real desert low-frequency noise to construct training set. In experiments, our method can raise the SNR of synthetic noisy data from -8.69 to 9.63 dB.

ADMM based low-rank and sparse matrix recovery method for sparse photoacoustic microscopy

Photoacoustic microscopy (PAM) has evolved into a new promising medical imaging tool available for both in vivo surficial and deep-tissue imaging with a high spatial resolution. However, the long data acquisition time has made real-time imaging highly challenging. This paper presents an Alternating Direction Method of Multipliers (ADMM) based low-rank and sparse matrix recovery method for a sparse optical-scanning PAM system to realize fast PAM vascular imaging.For our system, an x-y galvanometer scanner is used to achieve compressive sampling, and the associated image recovery process is formulated as a matrix completion problem. The sparse scanning scheme might be easy to integrate with several other optical-resolution PAM modalities. Further, the sparse constraint (the total variation norm) and the low-rank constraint (nuclear norm) are combined for solving the optimization program under ADMM framework for matrix recovery in order to achieve better PAM image recovery even for images that are not well-approximated by their low-rank components.A prototype PAM system has been implemented and the recovery method has been validated. From both visual effects and quantitative parameters, such as PSNR, SSIM, Rerr and MSE, comparable image qualities with conventional full sampling optical resolution PAM could be acquired by just half of the data acquisition time. Besides, the ADMM based low-rank and sparse matrix recovery method could show better results than GoDec. The obtained results demonstrate the preclinical and clinical potential of sparse PAM system in investigating vascular diseases.

Multi-Matrices Low-Rank Decomposition With Structural Smoothness for Image Denoising

In this paper, we propose a multi-matrices low-rank decomposition method for image denoising. In this new method, the total variation (TV) norm is incorporated into low-rank approximation analysis to achieve structural smoothness and to improve quality of the recovered images. Our proposed mathematical framework for multi-matrices low-rank decomposition combines the nuclear norm, TV norm, and $\mathcal {L}_{1}$ norm, which allows us to exploit the low-rank property of natural images, enhance the structural smoothness, and detect and remove large sparse noise. Based on the iterative alternating direction method, we develop an algorithm to solve the proposed challenging optimization problem. We conduct extensive experiments and perform evaluations on multi-images denoising and multi-frames video prediction. Our experimental results demonstrate that the proposed method outperforms the state-of-the-art low-rank matrix recovery methods, particularly for images with large sparse noise.

Reweighted Low-Rank Matrix Analysis With Structural Smoothness for Image Denoising.

In this paper, we develop a new low-rank matrix recovery algorithm for image denoising. We incorporate the total variation (TV) norm and the pixel range constraint into the existing reweighted low-rank matrix analysis to achieve structural smoothness and to significantly improve quality in the recovered image. Our proposed mathematical formulation of the low-rank matrix recovery problem combines the nuclear norm, TV norm, and norm, thereby allowing us to exploit the low-rank property of natural images, enhance the structural smoothness, and detect and remove large sparse noise. Using the iterative alternating direction and fast gradient projection methods, we develop an algorithm to solve the proposed challenging non-convex optimization problem. We conduct extensive performance evaluations on single-image denoising, hyper-spectral image denoising, and video background modeling from corrupted images. Our experimental results demonstrate that the proposed method outperforms the state-of-the-art low-rank matrix recovery methods, particularly for large random noise. For example, when the density of random sparse noise is 30%, for single-image denoising, our proposed method is able to improve the quality of the restored image by up to 4.21 dB over existing methods.

Semi-Automatic 2D-to-3D Conversion Using Low-Rank Matrix Recovery

Semi-automatic 2D-to-3D conversion is a promising solution to 3D stereoscopic content creation. However, the depth continuous transition between user marked neighboring regions will be lost when user scribbles are sparse. To help solve this problem, a piecewise-continuity regularized low-rank matrix recovery method is developed. Our approach is based on the fact that a depth-map can be decomposed into a low-rank matrix and an outlier term matrix. First, an initial dense depth-map is interpolated from the user scribbles using matting Laplacian scheme under the assumption that depth-map is piecewise-continuous. Second, a piecewise-continuity constrained low-rank recovery model is developed to remove outliers which are introduced by the interpolation. Experimental comparisons with existing algorithms show that our method demonstrates significant advantage over depth continuous transition between neighboring regions.

Pattern Synthesis for Sparse Arrays by Compressed Sensing and Low-Rank Matrix Recovery Methods

Antenna array pattern synthesis technology plays a vital role in the field of smart antennas. It is well known that the pattern synthesis of homogeneous array is the key topic of pattern synthesis technology. But this technology needs plenty of homogeneous array elements to meet the antenna requirements. So, a novel pattern synthesis technology for sparse array based on the compressed sensing (CS) and low-rank matrix recovery (LRMR) methods is proposed. The proposed technology predominantly includes the design of sparse array, the recovery of homogeneous array, and the synthesis of antenna array pattern. The simulation result shows that an antenna array with low gain and strong directivity can be arbitrarily built by the use of a small amount of sparse array elements and it is useful for the miniaturization and economical efficiency of the antenna system.

Improved low-rank matrix recovery method for predicting miRNA-disease association

MicroRNAs (miRNAs) performs crucial roles in various human diseases, but miRNA-related pathogenic mechanisms remain incompletely understood. Revealing the potential relationship between miRNAs and diseases is a critical problem in biomedical research. Considering limitation of existing computational approaches, we develop improved low-rank matrix recovery (ILRMR) for miRNA-disease association prediction. ILRMR is a global method that can simultaneously prioritize potential association for all diseases and does not require negative samples. ILRMR can also identify promising miRNAs for investigating diseases without any known related miRNA. By integrating miRNA-miRNA similarity information, disease-disease similarity information, and miRNA family information to matrix recovery, ILRMR performs better than other methods in cross validation and case studies.

Realistic action recognition with salient foreground trajectories

Human action recognition has great potential in many applications relevant to artificial intelligence, which can accelerate some research on expert and intelligent systems, such as feature selection. To improve the performance on human action recognition in realistic scenarios, a novel Salient Foreground Trajectory extraction method based on saliency detection and low-rank matrix recovery is proposed to learn the discriminative features from complicated video context. Specifically, a new trajectory saliency combining appearance saliency and motion saliency is proposed to divide the dense trajectories into salient trajectories and non-salient ones. The salient trajectories are approximately corresponding to the interested foreground region, while the non-salient subset is mainly composed of the dominating background trajectories. Furthermore, according to the low rank property of background motion, if the video has background motion, the background trajectory subspace is further constructed on the non-salient trajectory subset via low-rank matrix recovery method. Then the possible background trajectories in the salient subset could be subtracted. Finally, the resulting salient foreground trajectory features are encoded by the approach of Bag of Features or Fisher Vector for action classification. Experiments on KTH, UCF Sports and Olympic Sports have shown that the proposed Salient Foreground Trajectory method is effective and achieves comparable results to the state of the art.

Denoising time-resolved microscopy image sequences with singular value thresholding

Time-resolved imaging in microscopy is important for the direct observation of a range of dynamic processes in both the physical and life sciences. However, the image sequences are often corrupted by noise, either as a result of high frame rates or a need to limit the radiation dose received by the sample. Here we exploit both spatial and temporal correlations using low-rank matrix recovery methods to denoise microscopy image sequences. We also make use of an unbiased risk estimator to address the issue of how much thresholding to apply in a robust and automated manner. The performance of the technique is demonstrated using simulated image sequences, as well as experimental scanning transmission electron microscopy data, where surface adatom motion and nanoparticle structural dynamics are recovered at rates of up to 32 frames per second.

Texture Repairing by Unified Low Rank Optimization

In this paper, we show how to harness both low-rank and sparse structures in regular or near-regular textures for image completion. Our method is based on a unified formulation for both random and contiguous corruption. In addition to the low rank property of texture, the algorithm also uses the sparse assumption of the natural image: because the natural image is piecewise smooth, it is sparse in certain transformed domain (such as Fourier or wavelet transform). We combine low-rank and sparsity properties of the texture image together in the proposed algorithm. Our algorithm based on convex optimization can automatically and correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. This algorithm integrates texture rectification and repairing into one optimization problem. Through extensive simulations, we show our method can complete and repair textures corrupted by errors with both random and contiguous supports better than existing low-rank matrix recovery methods. Our method demonstrates significant advantage over local patch based texture synthesis techniques in dealing with large corruption, non-uniform texture, and large perspective deformation.

Automatic Arc Distortion Correction of Seismograms Using the Low-Rank Matrix Recovery Method

This letter presents a method of correcting the arc distortion of historical seismogram waveforms recorded by pen and paper drum-type seismographs. The proposed method employs the low-rank matrix recovery method to estimate deformation parameters and to correct geometrically distorted seismic waveforms. A seismogram is inherently regular and symmetrical, which motivates us to explore its textural properties. Given that rank is a natural measure of the regularity of textures and images, an undistorted seismogram texture is assumed to have a lower rank than its distorted versions. Thus, the proposed algorithm aims to find parameters that make the rank of the seismogram texture to the minimum. Compared with traditional methods, the proposed method can automatically estimate the parameters of recording devices and works efficiently and robustly.

Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to widely used time difference of arrival (TDOA) or correlation-based backprojection method. These methods work under the assumption that the scene is composed of a single or a few widely separated point targets. The new method overcomes this limitation and can reconstruct heterogeneous scenes with extended targets. We assume that the scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers and correlate the fast-time bistatic measurements at each slow-time. This correlation process maps the tensor product of the scene reflectivity with itself to the correlated measurements. Since this tensor product is a rank-one positive semi-definite operator, the image formation lends itself to low-rank matrix recovery techniques. Taking into account additive noise in bistatic measurements, we formulate the estimation of the rank-one operator as a convex optimization with rank constrain. We present a gradient-descent based iterative reconstruction algorithm and analyze its computational complexity. Extensive numerical simulations show that the new method is superior to correlation-based backprojection in reconstructing extended and distributed targets with better geometric fidelity, sharper edges, and better noise suppression.

Improved nonconvex optimization model for low-rank matrix recovery

Low-rank matrix recovery is an important problem extensively studied in machine learning, data mining and computer vision communities. A novel method is proposed for low-rank matrix recovery, targeting at higher recovery accuracy and stronger theoretical guarantee. Specifically, the proposed method is based on a nonconvex optimization model, by solving the low-rank matrix which can be recovered from the noisy observation. To solve the model, an effective algorithm is derived by minimizing over the variables alternately. It is proved theoretically that this algorithm has stronger theoretical guarantee than the existing work. In natural image denoising experiments, the proposed method achieves lower recovery error than the two compared methods. The proposed low-rank matrix recovery method is also applied to solve two real-world problems, i.e., removing noise from verification code and removing watermark from images, in which the images recovered by the proposed method are less noisy than those of the two compared methods.

Reweighted low-rank matrix recovery and its application in image restoration.

In this paper, we propose a reweighted low-rank matrix recovery method and demonstrate its application for robust image restoration. In the literature, principal component pursuit solves low-rank matrix recovery problem via a convex program of mixed nuclear norm and l1 norm. Inspired by reweighted l1 minimization for sparsity enhancement, we propose reweighting singular values to enhance low rank of a matrix. An efficient iterative reweighting scheme is proposed for enhancing low rank and sparsity simultaneously and the performance of low-rank matrix recovery is prompted greatly. We demonstrate the utility of the proposed method both on numerical simulations and real images/videos restoration, including single image restoration, hyperspectral image restoration, and background modeling from corrupted observations. All of these experiments give empirical evidence on significant improvements of the proposed algorithm over previous work on low-rank matrix recovery.

Multidimensional compressed sensing MRI using tensor decomposition-based sparsifying transform.

Compressed Sensing (CS) has been applied in dynamic Magnetic Resonance Imaging (MRI) to accelerate the data acquisition without noticeably degrading the spatial-temporal resolution. A suitable sparsity basis is one of the key components to successful CS applications. Conventionally, a multidimensional dataset in dynamic MRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the image sparsity. Traditional methods typically sparsify the spatial and temporal information independently. In this work, we propose a novel concept of tensor sparsity for the application of CS in dynamic MRI, and present the Higher-order Singular Value Decomposition (HOSVD) as a practical example. Applications presented in the three- and four-dimensional MRI data demonstrate that HOSVD simultaneously exploited the correlations within spatial and temporal dimensions. Validations based on cardiac datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods and, outperformed the conventional sparse recovery methods.