Compressive Signal Processing with Circulant Sensing Matrices

Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises of processing the random projections directly, without first reconstructing the signal. In this paper, we show that circulant sensing matrices allow to perform a variety of classical signal processing tasks such as filtering, interpolation, registration, transforms, and so forth, directly in the compressed domain and in an exact fashion, \emph{i.e.}, without relying on estimators as proposed in the existing literature. The advantage of the techniques presented in this paper is to enable direct measurement-to-measurement transformations, without the need of costly recovery procedures

Microscopy without Imaging: Compressive Sensing for Heart-synchronized Imaging

We demonstrate experimentally that direct analysis of compressively sensed signals provides sufficient information to achieve high-precision phase lock to a periodicallymoving structure, without any need to ever reconstruct an image of the target object

A Kosambi-Karhunen–Loève Learning Approach to Cooperative Spectrum Sensing in Cognitive Radio Networks

This paper focuses on the issues of cooperative spectrum sensing (CSS) in a large cognitive radio network (CRN) where cognitive radio (CR) nodes can cooperative with neighboring nodes using spatial cooperation. A novel optimal global primary user (PU) detection framework with geographical cooperation using a deflection coefficient metric measure to characterize detection performance is proposed. It is assumed that only a small fraction of CR nodes communicate with the fusion center (FC). Optimal cooperative techniques which are global for class deterministic PU signals are proposed. By establishing the relationship between the CSS technique design issues and Kosambi-Karhunen–Loève transform (KLT) the problem is solved efficiently and the impact on detection performance is evaluated using simulation.Peer reviewedFinal Accepted Versio

A Short Note on Compressed Sensing with Partially Known Signal Support

This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The reconstruction method is based on a convex minimization program coined "innovative Basis Pursuit DeNoise" (or iBPDN). Under the common $\ell_2$-fidelity constraint made on the available measurements, this optimization promotes the ($\ell_1$) sparsity of the candidate signal over the complement of this known part. In particular, this paper extends the results of Vaswani et al. to the cases of compressible signals and noisy measurements. Our proof relies on a small adaption of the results of Candes in 2008 for characterizing the stability of the Basis Pursuit DeNoise (BPDN) program. We emphasize also an interesting link between our method and the recent work of Davenport et al. on the $\delta$-stable embeddings and the "cancel-then-recover" strategy applied to our problem. For both approaches, reconstructions are indeed stabilized when the sensing matrix respects the Restricted Isometry Property for the same sparsity order. We conclude by sketching an easy numerical method relying on monotone operator splitting and proximal methods that iteratively solves iBPDN