We consider the problem of recovering clustered sparse signals with no prior knowledge of the sparsity pattern. Beyond simple sparsity, signals of interest often exhibits an underlying sparsity pattern which, if leveraged, can improve the reconstruction performance. However, the sparsity pattern is usually unknown a priori. Inspired by the idea of k-nearest neighbor (k-NN) algorithm, we propose...

We study the sparsity of spectro-temporal representation of speech in reverberant acoustic conditions. This study motivates the use of structured sparsity models for efficient speech recovery. We formulate the underdetermined convolutive speech separation in spectro-temporal domain as the sparse signal recovery where we leverage model-based recovery algorithms. To tackle the ambiguity of the re...

The problem of consistently estimating the sparsity pattern of a vector β∗ ∈ R based on observations contaminated by noise arises in various contexts, including signal denoising, sparse approximation, compressed sensing, and model selection. We analyze the behavior of l1-constrained quadratic programming (QP), also referred to as the Lasso, for recovering the sparsity pattern. Our main result i...

We discuss a general notion of “sparsity structure” and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the “usual sparsity” and “usual l1 recovery,” (b) block-sparsity with possibly overlapping blocks and associated block-l1 recovery, and (c) low-rank-oriented recovery by nuclear...

The algorithms based on the technique of optimal $k$-thresholding (OT) were recently proposed for signal recovery, and they are very different from traditional family hard thresholding methods. However, computational cost OT-based remains high at current stage their development. This stimulates development so-called natural ...

We consider the Compressed Sensing problem. We have a large under-determined set of noisy measurements Y = GX+N, where X is a sparse signal and G is drawn from a random ensemble. In our previous work, we had shown that a signal-to-noise ratio, SNR = O(log n) is necessary and sufficient for support recovery from an information-theoretic perspective. In this paper we present a linear programming ...