SPARSITY-BASED REPRESENTATION WITH LOW-RANK INTERFERENCE: ALGORITHMS AND APPLICATIONS

Sparse representation;low-rank;joint sparsity;group sparsity;multi-sensor;speech recognition;hyperspectral;SAR;facial expression recognition;kernel;classification;reconstruction;Electrical Engineering

Dao, Minh D.Tran, Trac Duy ;

Johns Hopkins University

关键词: Sparse representation;    low-rank;    joint sparsity;    group sparsity;    multi-sensor;    speech recognition;    hyperspectral;    SAR;    facial expression recognition;    kernel;    classification;    reconstruction;    Electrical Engineering;   

Others  :  https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/39357/DAO-DISSERTATION-2015.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: JOHNS HOPKINS DSpace Repository

【 摘 要 】

In this thesis, we develop a novel general framework that is capable of extracting a low-rank interference while simultaneously promoting sparsity-based representation of multiple correlated signals. The proposed framework provides a new and efficient approach for the representation of multiple measurements where the underlying signals exhibit a structured sparsity representation over some proper dictionaries but are corrupted by the interference from external sources. Under the assumption that the interference component forms a low-rank structure, the proposed algorithms minimize the nuclear norm of the interference to exclude it from the representation of multivariate sparse representation. In other words, this thesis investigates the problem of structural sparse signal representation even in the presence of large but correlated noise/interference. A fast and efficient algorithm based on alternating direction methods of multipliers (ADMM) approach is studied to solve the convex optimization problems arisen from these models. Furthermore, we modify the classical ADMM approach by utilizing an approximation to relax the dictionary transform representation, thus simplify the computing efforts to achieve optimization solutions. By this modification, we further show that the algorithm is guaranteed to converge to the global optimum solutions. Extensive experiments are conducted on four practical applications: (i) synthetic aperture radar image recovery, (ii) hyperspectral chemical plume detection and classification, (iii) robust speech recognition in noisy environments, and (iv) video-based facial expression recognition; all of which show that the proposed models provide significant improved performance compared with the state-of-the-art results.The thesis further extends the general simultaneous structured sparsity and low-rank framework to multi-sensor for classification problems. Particularly, we study a variety of novel sparsity-regularized regression methods, commonly categorized as collaborative multi-sensor sparse representation for classification, which effectively incorporates simultaneous structured-sparsity constraints, demonstrated via a row-sparse and/or block-sparse coefficient matrix, both within each sensor and across multiple heterogeneous sensors. The efficacy of the proposed multi-sensor algorithms is verified in an automatic border patrol control application to discriminate between human and animal footsteps.