Distributed Compressive Sensing (DCS) studies the recovery of jointly sparse signals. Compared to separate recovery, the joint recovery algorithms in DCS are usually more effective as they make use of the joint sparsity. In this thesis, we study a weighted l1-minimization algorithm for the joint sparsity model JSM-1 proposed by Baron et al. Our analysis gives a sufficient null space property fo...

We develop a novel sparse low-rank block (SLoB) signal recovery framework that simultaneously exploits sparsity and low-rankness to accurately identify peptides (fragments of proteins) from biological samples via tandem mass spectrometry (TMS). To efficiently perform SLoB-based peptide identification, we propose two novel recovery algorithms, an exact iterative method and an approximate greedy ...

We study classic streaming and sparse recovery problems using deterministic linear sketches, including `1/`1 and `∞/`1 sparse recovery problems, norm estimation, and approximate inner product. We focus on devising a fixed matrix A ∈ Rm×n and a deterministic recovery/estimation procedure which work for all possible input vectors simultaneously. We contribute several improved bounds for these pro...

OF THE CAPSTONE PROJECT Sparse Image and Video Recovery Using Gradient Projection for Linearly Constrained Convex Optimization by Daniel Thompson May 2011 University of California, Merced Abstract This project concerns the reconstruction of a signal, which corresponds to either an image or a temporally-varying scene. Signal recovery can be accomplished through finding a sparse solution to an `2...

Both L1/2 and L2/3 are two typical non-convex regularizations of Lp (0<p<1), which can be employed to obtain a sparser solution than the L₁ regularization. Recently, the multiple-state sparse transformation strategy has been developed to exploit the sparsity in L₁ regularization for sparse signal recovery, which combines the iterative reweighted algorithms. To further exploit the sparse structu...

In this paper, a novel algorithm, Cross Low-dimension Pursuit, based on a new structured sparse matrix, Permuted Block Diagonal (PBD) matrix, is proposed in order to recover sparse signals from incomplete linear measurements. The main idea of the proposed method is using the PBD matrix to convert a high-dimension sparse recovery problem into two (or more) groups of highly low-dimension problems...

Unions of subspaces provide a powerful generalization of single subspace models for collections of high-dimensional data; however, learning multiple subspaces from data is challenging due to the fact that segmentation—the identification of points that live in the same subspace—and subspace estimation must be performed simultaneously. Recently, sparse recovery methods were shown to provide a pro...

The standard compressive sensing (CS) aims to recover sparse signal from single measurement vector which is known as SMV model. By contrast, recovery of sparse signals from multiple measurement vectors is called MMV model. In this paper, we consider the recovery of jointly sparse signals in the MMV model where multiple signal measurements are represented as a matrix and the sparsity of signal o...

Unions of subspaces provide a powerful generalization of single subspace models for collections of high-dimensional data; however, learning multiple subspaces from data is challenging due to the fact that segmentation—the identification of points that live in the same subspace—and subspace estimation must be performed simultaneously. Recently, sparse recovery methods were shown to provide a pro...

The new emerging theory of compressive sampling demonstrates that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate—using random projections—and achieve perfect reconstruction. In this paper, we consider a special case of compressive sampling where the uncompressed signal is non-negative, and propose a number of sparse recovery algorithms—which ut...