Sparse approximation

About: Sparse approximation is a research topic. Over the lifetime, 18037 publications have been published within this topic receiving 497739 citations. The topic is also known as: Sparse approximation.

Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation

Abstract: The l1 regularized Gaussian maximum likelihood estimator has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the resulting optimization problem which is a regularized log-determinant program. In contrast to other state-of-the-art methods that largely use first order gradient information, our algorithm is based on Newton's method and employs a quadratic approximation, but with some modifications that leverage the structure of the sparse Gaussian MLE problem. We show that our method is superlinearly convergent, and also present experimental results using synthetic and real application data that demonstrate the considerable improvements in performance of our method when compared to other state-of-the-art methods.

Metaface learning for sparse representation based face recognition

Abstract: Face recognition (FR) is an active yet challenging topic in computer vision applications. As a powerful tool to represent high dimensional data, recently sparse representation based classification (SRC) has been successfully used for FR. This paper discusses the metaface learning (MFL) of face images under the framework of SRC. Although directly using the training samples as dictionary bases can achieve good FR performance, a well learned dictionary matrix can lead to higher FR rate with less dictionary atoms. An SRC oriented unsupervised MFL algorithm is proposed in this paper and the experimental results on benchmark face databases demonstrated the improvements brought by the proposed MFL algorithm over original SRC.

Sparse Vector Methods

Abstract: Sparse vector methods enhance the efficiency of matrix solution algorithms by exploiting the sparsity of the independent vector and/or the desire to know only a subset of the unknown vector. This paper shows how these methods can be efficiently implemented for sparse matrices. The efficiency of the sparse vector methods is verified by tests on a 156-bus, a 1598-bus and a 2265-bus system. In all cases tested, the new methods are significantly faster than the established sparse matrix techniques.

GESPAR: Efficient Phase Retrieval of Sparse Signals

Abstract: We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of Fourier phase information, this problem is ill-posed. Therefore, prior information on the signal is needed in order to enable its recovery. In this work we consider the case in which the signal is known to be sparse, i.e., it consists of a small number of nonzero elements in an appropriate basis. We propose a fast local search method for recovering a sparse signal from measurements of its Fourier transform (or other linear transform) magnitude which we refer to as GESPAR: GrEedy Sparse PhAse Retrieval. Our algorithm does not require matrix lifting, unlike previous approaches, and therefore is potentially suitable for large scale problems such as images. Simulation results indicate that GESPAR is fast and more accurate than existing techniques in a variety of settings.

Underdetermined blind source separation based on sparse representation

Abstract: This paper discusses underdetermined (i.e., with more sources than sensors) blind source separation (BSS) using a two-stage sparse representation approach. The first challenging task of this approach is to estimate precisely the unknown mixing matrix. In this paper, an algorithm for estimating the mixing matrix that can be viewed as an extension of the DUET and the TIFROM methods is first developed. Standard clustering algorithms (e.g., K-means method) also can be used for estimating the mixing matrix if the sources are sufficiently sparse. Compared with the DUET, the TIFROM methods, and standard clustering algorithms, with the authors' proposed method, a broader class of problems can be solved, because the required key condition on sparsity of the sources can be considerably relaxed. The second task of the two-stage approach is to estimate the source matrix using a standard linear programming algorithm. Another main contribution of the work described in this paper is the development of a recoverability analysis. After extending the results in , a necessary and sufficient condition for recoverability of a source vector is obtained. Based on this condition and various types of source sparsity, several probability inequalities and probability estimates for the recoverability issue are established. Finally, simulation results that illustrate the effectiveness of the theoretical results are presented.