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 ...

RAYKO I. STANTCHEV,* DAVID B. PHILLIPS, PETER HOBSON, SAMUEL M. HORNETT, MILES J. PADGETT, AND EUAN HENDRY School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK QinetiQ Limited, Cody Technology Park, Ively Road, Farnborough GU14 0LX, UK e-mail: [email protected] *Corresponding author: ris20...

We consider a class of approximated message passing (AMP) algorithms and characterize their high-dimensional behavior in terms of a suitable state evolution recursion. Our proof applies to Gaussian matrices with independent but not necessarily identically distributed entries. It covers – in particular– the analysis of generalized AMP, introduced by Rangan, and of AMP reconstruction in compresse...

A challenging problem in security is the screening of cargo. The greater size, density, and complexity of cargo makes CT-based sensing especially diffi cult. These problems are compounded when sensing geometry is limited. In this project, we aim to develop accurate physics-based models of X-ray cargo sensing and corresponding model-based image reconstruction methods for limited angle measuremen...

Recall the setup in compressive sensing. There is an unknown signal z ∈ R, and we can only glean information about z through linear measurements. We choose m linear measurements a1, . . . , am ∈ R. “Nature” then chooses a signal z, and we receive the results b1 = 〈a1, z〉, . . . , bm = 〈am, z〉 of our measurements, when applied to z. The goal is then to recover z from b. Last lecture culminated i...

Introduction k-t GRAPPA [1,2,3] has been proposed for dynamic imaging with high reduction factors. In this work, GRAPPA operator [4] and narrow window data sharing are used to significantly improve the accuracy and reconstruction speed of k-t GRAPPA. The enhanced version is called the second generation (2G) k-t GRAPPA. Experiments with cardiac cine data sets show that the 2G k-t GRAPPA can prod...