Sparsity-based Methods Research Articles

A new mixing matrix estimation method based on the geometrical analysis of the sound separation problem

Nowadays, some of the most successful sound source separation methods are based on the assumption of sparse sources. A large number of those separation solutions consist of two parts: the mixing matrix estimation and the separation stages. Concerning the first part, many sparsity-based separation methods rely on the use of clustering techniques to identify the samples of the mixtures due to each sound source. With certain types of sources, such as speech, the assumption of sparsity is questionable and so, these stages do not perform correctly.In this paper, we present a new mixing matrix estimation procedure to overcome sparsity-based methods separating speech sources. Our novel proposal establishes a geometric relationship between the mixing parameters using some available information about the microphone array, such as, number and type of microphones or the distance between them. Using this relationship, the complex estimation of the level differences is avoided. Results demonstrate that our proposal outperforms mixing matrix estimation solutions in terms of both speech separation quality and speech intelligibility.

A robust sparse-modeling framework for estimating schizophrenia biomarkers from fMRI

BackgroundOur goal is to identify the brain regions most relevant to mental illness using neuroimaging. State of the art machine learning methods commonly suffer from repeatability difficulties in this application, particularly when using large and heterogeneous populations for samples. New methodWe revisit both dimensionality reduction and sparse modeling, and recast them in a common optimization-based framework. This allows us to combine the benefits of both types of methods in an approach which we call unambiguous components. We use this to estimate the image component with a constrained variability, which is best correlated with the unknown disease mechanism. ResultsWe apply the method to the estimation of neuroimaging biomarkers for schizophrenia, using task fMRI data from a large multi-site study. The proposed approach yields an improvement in both robustness of the estimate and classification accuracy. Comparison with existing methodsWe find that unambiguous components incorporate roughly two thirds of the same brain regions as sparsity-based methods LASSO and elastic net, while roughly one third of the selected regions differ. Further, unambiguous components achieve superior classification accuracy in differentiating cases from controls. ConclusionsUnambiguous components provide a robust way to estimate important regions of imaging data.

Comparative analysis of autofocus functions in digital in-line phase-shifting holography.

Numerical reconstruction of digital holograms relies on a precise knowledge of the original object position. However, there are a number of relevant applications where this parameter is not known in advance and an efficient autofocusing method is required. This paper addresses the problem of finding optimal focusing methods for use in reconstruction of digital holograms of macroscopic amplitude and phase objects, using digital in-line phase-shifting holography in transmission mode. Fifteen autofocus measures, including spatial-, spectral-, and sparsity-based methods, were evaluated for both synthetic and experimental holograms. The Fresnel transform and the angular spectrum reconstruction methods were compared. Evaluation criteria included unimodality, accuracy, resolution, and computational cost. Autofocusing under angular spectrum propagation tends to perform better with respect to accuracy and unimodality criteria. Phase objects are, generally, more difficult to focus than amplitude objects. The normalized variance, the standard correlation, and the Tenenbaum gradient are the most reliable spatial-based metrics, combining computational efficiency with good accuracy and resolution. A good trade-off between focus performance and computational cost was found for the Fresnelet sparsity method.

Sparse continuous-field and super-resolution method for direction-of-arrival estimation

In the application of direction-of-arrival (DOA) estimation based on sensor array, bearing-discretization has been a major technique for the sparsity-based methods in the past decade. However, discretization leads to the modeling error of sparse representation, which usually deteriorates the accuracy of DOA estimation. In this paper, a sparse continuous-field and super-resolution method (SCSM) is proposed to overcome the discretization issue. SCSM estimates DOA in the continuous bearing-space by solving a minimization problem, which combines the measurement covariance fitting criterion with the source-sparsity constraint characterized by minimizing an atomic norm. This minimization problem has a unique solution. After obtained the solution uniquely, Prony's method is utilized to estimate the DOA of sources. Therefore, SCSM has the capability to acquire a sparse and accurate estimation of DOA. In addition, it has some other advantages, including excellent super-resolution capability, no requirement of source number, applicability to arbitrary number of snapshots. Numerical results demonstrate the superior performance of the presented method.

FIR‐filter‐based method for the calibration of model errors in wideband digital array radar

Wideband digital array radar (WDAR) has the potential of achieving high resolution and providing multi-function simultaneously, but it is limited in practical use due to the effects of frequency-dependent array model errors. A method to jointly calibrate gain-phase perturbations and mutual coupling effects in WDRA is presented. First, a sparse-based method is deployed to calculate the narrowband calibration matrices at a set of discrete frequencies. Moreover, using a group of finite-impulse response filters, a wideband calibration matrix is constructed, which is capable of compensating the imperfections of array at any frequency in the band. The proposed method is simple and feasible for actual applications, which can be applied to arbitrary array geometries. Simulations and experimental results with measured data demonstrate the validity and effectiveness of the proposed method.

Abnormal Event Detection via Compact Low-Rank Sparse Learning

Sparsity-based methods have been recently applied to abnormal event detection, and have achieved impressive results. However, most such methods fail to consider the relationship among coefficient vectors; furthermore, they neglect the underlying "dictionary structure."' The authors' compact low-rank sparse representation (CLSR) method overcomes these drawbacks. Specifically, it adds compact regularization to the sparse representation model, which explicitly considers the relationship among coefficient vectors. The authors utilize the low-rank property to capture the underlying dictionary structure. Their method is verified on three challenging databases, and the experimental results demonstrate that it compares favorably to state-of-the-art methods in abnormal event detection.

Image Super-Resolution Based on Structure-Modulated Sparse Representation

Sparse representation has recently attracted enormous interests in the field of image restoration. The conventional sparsity-based methods enforce sparse coding on small image patches with certain constraints. However, they neglected the characteristics of image structures both within the same scale and across the different scales for the image sparse representation. This drawback limits the modeling capability of sparsity-based super-resolution methods, especially for the recovery of the observed low-resolution images. In this paper, we propose a joint super-resolution framework of structure-modulated sparse representations to improve the performance of sparsity-based image super-resolution. The proposed algorithm formulates the constrained optimization problem for high-resolution image recovery. The multistep magnification scheme with the ridge regression is first used to exploit the multiscale redundancy for the initial estimation of the high-resolution image. Then, the gradient histogram preservation is incorporated as a regularization term in sparse modeling of the image super-resolution problem. Finally, the numerical solution is provided to solve the super-resolution problem of model parameter estimation and sparse representation. Extensive experiments on image super-resolution are carried out to validate the generality, effectiveness, and robustness of the proposed algorithm. Experimental results demonstrate that our proposed algorithm, which can recover more fine structures and details from an input low-resolution image, outperforms the state-of-the-art methods both subjectively and objectively in most cases.

Practical comparison of sparse methods for classification of Arabica and Robusta coffee species using near infrared hyperspectral imaging

In the present work sparse-based methods are applied to the analysis of hyperspectral images with the aim at studying their capability of being adequate methods for variable selection in a classification framework. The key aspect of sparse methods is the possibility of performing variable selection by forcing the model coefficients related to irrelevant variables to zero. In particular, two different sparse classification approaches, i.e. sPCA+kNN and sPLS-DA, were compared with the corresponding classical methods (PCA+kNN and PLS-DA) to classify Arabica and Robusta coffee species. Green coffee samples were analyzed using near infrared hyperspectral imaging and the average spectra from each hyperspectral image were used to build training and test sets; furthermore a test image was used to evaluate the performances of the considered methods at pixel-level. In our case, sparse methods led to similar results as classical methods, with the advantage of obtaining more interpretable and parsimonious models. An important result to highlight is that variable selection performed with two different sparse classification approaches converged to the selection of same spectral regions, which implies the chemical relevance of those regions in the discrimination of Arabica and Robusta coffee species.

Local Sparse Structure Denoising for Low-Light-Level Image.

Sparse and redundant representations perform well in image denoising. However, sparsity-based methods fail to denoise low-light-level (LLL) images because of heavy and complex noise. They consider sparsity on image patches independently and tend to lose the texture structures. To suppress noises and maintain textures simultaneously, it is necessary to embed noise invariant features into the sparse decomposition process. We, therefore, used a local structure preserving sparse coding (LSPSc) formulation to explore the local sparse structures (both the sparsity and local structure) in image. It was found that, with the introduction of spatial local structure constraint into the general sparse coding algorithm, LSPSc could improve the robustness of sparse representation for patches in serious noise. We further used a kernel LSPSc (K-LSPSc) formulation, which extends LSPSc into the kernel space to weaken the influence of linear structure constraint in nonlinear data. Based on the robust LSPSc and K-LSPSc algorithms, we constructed a local sparse structure denoising (LSSD) model for LLL images, which was demonstrated to give high performance in the natural LLL images denoising, indicating that both the LSPSc- and K-LSPSc-based LSSD models have the stable property of noise inhibition and texture details preservation.

Motion parameter estimation of multiple ground moving targets in multi-static passive radar systems

Abstract Multi-static passive radar (MPR) systems typically use narrowband signals and operate under weak signal conditions, making them difficult to reliably estimate motion parameters of ground moving targets. On the other hand, the availability of multiple spatially separated illuminators of opportunity provides a means to achieve multi-static diversity and overall signal enhancement. In this paper, we consider the problem of estimating motion parameters, including velocity and acceleration, of multiple closely located ground moving targets in a typical MPR platform with focus on weak signal conditions, where traditional time-frequency analysis-based methods become unreliable or infeasible. The underlying problem is reformulated as a sparse signal reconstruction problem in a discretized parameter search space. While the different bistatic links have distinct Doppler signatures, they share the same set of motion parameters of the ground moving targets. Therefore, such motion parameters act as a common sparse support to enable the exploitation of group sparsity-based methods for robust motion parameter estimation. This provides a means of combining signal energy from all available illuminators of opportunity and, thereby, obtaining a reliable estimation even when each individual signal is weak. Because the maximum likelihood (ML) estimation of motion parameters involves a multi-dimensional search and its performance is sensitive to target position errors, we also propose a technique that decouples the target motion parameters, yielding a two-step process that sequentially estimates the acceleration and velocity vectors with a reduced dimensionality of the parameter search space. We compare the performance of the sequential method against the ML estimation with the consideration of imperfect knowledge of the initial target positions. The Cramér-Rao bound (CRB) of the underlying parameter estimation problem is derived for a general multiple-target scenario in an MPR system. Simulation results are provided to compare the performance of the sparse signal reconstruction-based methods against the traditional time-frequency-based methods as well as the CRB.

A Novel Sparsity-Based Framework Using Max Pooling Operation for Hyperspectral Image Classification

Various sparsity-based methods have been widely used in hyperspectral image (HSI) classification. To determine the class label of a test sample, traditional sparsity-based frameworks mainly use the sparse vectors to compute the residual error for classification. In this paper, a novel sparsity-based framework is proposed, which adopts the max pooling operation for HSI classification. Compared with the traditional sparsity-based frameworks using residual error, sparse vectors in our proposed framework are utilized to generate the feature vectors using max pooling operation. Experimental results demonstrate that our proposed framework can achieve the state-of-the-art classification performance.

Sparsity-Driven Synthetic Aperture Radar Imaging: Reconstruction, autofocusing, moving targets, and compressed sensing

This article presents a survey of recent research on sparsity-driven synthetic aperture radar (SAR) imaging. In particular, it reviews 1) the analysis and synthesis-based sparse signal representation formulations for SAR image formation together with the associated imaging results, 2) sparsity-based methods for wide-angle SAR imaging and anisotropy characterization, 3) sparsity-based methods for joint imaging and autofocusing from data with phase errors, 4) techniques for exploiting sparsity for SAR imaging of scenes containing moving objects, and 5) recent work on compressed sensing (CS)-based analysis and design of SAR sensing missions.

Sparse Signal Recovery for Direction-of-Arrival Estimation Based on Source Signal Subspace

After establishing the sparse representation of the source signal subspace, we propose a new method to estimate the direction of arrival (DOA) by solving anℓ1-norm minimization for sparse signal recovery of the source powers. Second-order cone programming is applied to reformulate this optimization problem, and it is solved effectively by employing the interior point method. Due to the keeping of the signal subspace and the discarding of the noise subspace, the proposed method is more robust to noise than many other sparsity-based methods. The real data tests and the numerical simulations demonstrate that the proposed method has improved accuracy and robustness to noise, and it is not sensitive to the knowledge about the number of sources. We discuss the computational cost of our method theoretically, and the experiment results verify the computational effectiveness.

Frequency Estimation of Irregularly Sampled Data Using a Sparsity Constrained Weighted Least-Squares Approach

In this paper, a new method for frequency estimation of irregularly sampled data is proposed. In comparison with the previous sparsity-based methods where the sparsity constraint is applied to a least-squares fitting problem, the proposed method is based on a sparsity constrained weighted least-squares problem. The resulting problem is solved in an iterative manner, allowing the usage of the solution obtained at each iteration to determine the weights of the least-squares fitting term at the next iteration. Such an appropriate weighting of the least-squares fitting term enhances the performance of the proposed method. Simulation results verify that the proposed method can detect the spectral peaks using a very short data record. Compared to the previous one, the proposed method is less probable to miss the actual spectral peaks and exhibit spurious peaks.

Context-Aware Sparse Decomposition for Image Denoising and Super-Resolution

Image prior models based on sparse and redundant representations are attracting more and more attention in the field of image restoration. The conventional sparsity-based methods enforce sparsity prior on small image patches independently. Unfortunately, these works neglected the contextual information between sparse representations of neighboring image patches. It limits the modeling capability of sparsity-based image prior, especially when the major structural information of the source image is lost in the following serious degradation process. In this paper, we utilize the contextual information of local patches (denoted as context-aware sparsity prior) to enhance the performance of sparsity-based restoration method. In addition, a unified framework based on the markov random fields model is proposed to tune the local prior into a global one to deal with arbitrary size images. An iterative numerical solution is presented to solve the joint problem of model parameters estimation and sparse recovery. Finally, the experimental results on image denoising and super-resolution demonstrate the effectiveness and robustness of the proposed context-aware method.

Moving Object Detection by Detecting Contiguous Outliers in the Low-Rank Representation

Object detection is a fundamental step for automated video analysis in many vision applications. Object detection in a video is usually performed by object detectors or background subtraction techniques. Often, an object detector requires manually labeled examples to train a binary classifier, while background subtraction needs a training sequence that contains no objects to build a background model. To automate the analysis, object detection without a separate training phase becomes a critical task. People have tried to tackle this task by using motion information. But existing motion-based methods are usually limited when coping with complex scenarios such as nonrigid motion and dynamic background. In this paper, we show that the above challenges can be addressed in a unified framework named DEtecting Contiguous Outliers in the LOw-rank Representation (DECOLOR). This formulation integrates object detection and background learning into a single process of optimization, which can be solved by an alternating algorithm efficiently. We explain the relations between DECOLOR and other sparsity-based methods. Experiments on both simulated data and real sequences demonstrate that DECOLOR outperforms the state-of-the-art approaches and it can work effectively on a wide range of complex scenarios.