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The thresholded feature has recently emerged as an extremely efficient, yet rough empirical approximation, of the time-consuming sparse coding inference process. Such an approximation has not yet been rigorously examined, and standard…
This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we…
Distributed compressed sensing is concerned with representing an ensemble of jointly sparse signals using as few linear measurements as possible. Two novel joint reconstruction algorithms for distributed compressed sensing are presented in…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…
Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
It is well-established that many iterative sparse reconstruction algorithms can be unrolled to yield a learnable neural network for improved empirical performance. A prime example is learned ISTA (LISTA) where weights, step sizes and…
Sparse coding of images is traditionally done by cutting them into small patches and representing each patch individually over some dictionary given a pre-determined number of nonzero coefficients to use for each patch. In lack of a way to…
In this paper we propose a distributed iterated hard thresholding algorithm termed DiFIGHT over a network that is built on the diffusion mechanism and also propose a modification of the proposed algorithm, termed MoDiFIGHT, that has low…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
Spectrum sensing is an important process in cognitive radio. A number of sensing techniques that have been proposed suffer from high processing time, hardware cost and computational complexity. To address these problems, compressive sensing…