Adaptive sensing strategies have been proven to outperform traditional (non adaptive) compressed sensing, in terms of the signal to noise ratios that can be handled, and/or the number of measurements needed to accurately recover a signal of interest. Most existing adaptive sensing schemes for sparse signals, while work well in practice, do not take into account potential structure present in th...

We consider the problem of reconstructing a sparse signal x0 ∈ R from a limited number of linear measurements. Given m randomly selected samples of Ux0, where U is an orthonormal matrix, we show that 1 minimization recovers x0 exactly when the number of measurements exceeds m const · μ(U) · S · log n, where S is the number of nonzero components in x0 and μ is the largest entry in U properly nor...

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The extremely high sampling rate is a challenge for ultra-wideband (UWB) communication. In this paper, we study the compressed sensing (CS) based impulse radio UWB (IR-UWB) signal detection and propose an IR-UWB signal detection algorithm based on compressive sampling matching pursuit (CoSaMP). The proposed algorithm relies on the fact that UWB received signal is sparse in the time domain. The ...

Distributed compressed sensing is the extension of compressed sampling (CS) to sensor networks. The idea is to design a CS joint decoding scheme at a central decoder (base station) that exploits the inter-sensor correlations, in order to recover the whole observations from very few number of random measurements per node. In this paper, we focus on modeling the correlations and on the design and...

A new theory named compressed sensing for simultaneous sampling and compression of signals has been becoming popular in the communities of signal processing, imaging and applied mathematics. In this paper, we present improved/accelerated iterative curvelet thresholding methods for compressed sensing reconstruction in the fields of remote sensing. Some recent strategies including Bioucas-Dias an...

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate an...

Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to address this issue. It was justified recently from a theoretical point of view in the compressed sensing (CS) literature. Unfortunately, the sampling schemes suggested by current CS theories may not be relevant since they do not take the acq...

MIMO array can obtain much more equivalent elements by using a small number of transmitters and receivers. However, according to traditional sampling theorem, a certain number of transmitters and receivers are still needed to obtain a dense equivalent array. Since the interesting targets of ground penetrating radar (GPR) are usually sparse, this paper presents a spare MIMO array GPR imaging sch...

Signal processing techniques have been developed that use different strategies to bypass the Nyquist sampling theorem in order to recover more information than a traditional discrete Fourier transform. Here we examine three such methods: filter diagonalization, compressed sensing, and super-resolution. We apply them to a broad range of signal forms commonly found in science and engineering in o...