Compressive sensing (CS) exploits the sparsity present in many signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in environments where the input ...

An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon, and demonstrating how it can be fruitfully exploited by the design of suitable sampling strategies in order to outperform more standard compressed sensing tech...

Performance guarantees for recovery algorithms employed in sparse representations, and compressed sensing highlights the importance of incoherence. Optimal bounds of incoherence are attained by equiangular unit norm tight frames (ETFs). Although ETFs are important in many applications, they do not exist for all dimensions, while their construction has been proven extremely difficult. In this pa...

We study the recovery results of lp-constrained compressive sensing (CS) with p ≥ 1 via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon (2014) from l2-constrained CS to lp-constrained case with p ≥ 1 and complements the reco...

This paper designs and evaluates a variant of CoSaMP algorithm, for recovering the sparse signal s from the compressive measurement ( ) v Uw s   given a fixed lowrank subspace spanned by U. Instead of firstly recovering the full vector then separating the sparse part from the structured dense part, the proposed algorithm directly works on the compressive measurement to do the separation. We i...

We introduce and analyze a framework for function interpolation using compressed sensing. This framework – which is based on weighted l minimization – does not require a priori bounds on the expansion tail in either its implementation or its theoretical guarantees. Moreover, in the absence of noise it leads to genuinely interpolatory approximations. We also establish a series of new recovery gu...

Recent results in compressed sensing have shown that a wide variety of structured signals can be recovered from undersampled and noisy linear observations. In this paper, we show that many of these signal structures can be modeled using an union of affine subspaces, and that the fundamental number of observations needed for stable recovery is given by the number of “free” values, i.e. the dimen...

—With marine development thriving today, underwater acoustic sensor networks have become a vital method in exploring and monitoring the ocean. In this paper, a data recovery scheme with adaptive resolution based on compressed sensing theory is proposed, aiming at acclimating to the atrocious conditions under the water. The fundamental thought of the scheme is to achieve better quality of recov...

In contrast to the vast amount of literature in random matrices in the field of compressed sensing, the subject of deterministic matrix design is at its early stages. Since these deterministic matrices are usually constructed using the polynomials in finite Galois fields, the number of rows (number of samples) is restricted to some specific integers such as prime powers. In this paper, besides ...