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...

We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The reconstruction method relies on the recently demonstrated sparsity-based sub-wavelength imaging. However, for partially-spatially-incoherent light, the relation bet...

We extend ideas from compressive sensing to a structured sparsity model related to fusion frames. We present theoretical results concerning the recovery of sparse signals in a fusion frame from undersampled measurements. We provide both nonuniform and uniform recovery guarantees. The novelty of our work is to exploit an incoherence property of the fusion frame which allows us to reduce the numb...

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in [1] to recover 1-dimensional spectrally sparse signal. However, in spite of existing research efforts [2], ...

The problem of imaging periodic structure (source or scatterer) is formulated in the framework of compressed sensing with special attention on subwavelength resolution. It is shown that in this formulation the subwavelength resolution in the presence of noise can not be achieved by compressed sensing techniques alone. Additional techniques such as near-field measurement or illumination are requ...

The analysis of ISAR image recovery from a reduced set of data presented in [1] is extended in this correspondence to an important topic of signal nonsparsity (approximative sparsity). In real cases the ISAR images are noisy and only approximately sparse. Formula for the mean square error in the nonsparse ISAR, reconstructed under the sparsity assumption, is derived. The results are tested on e...