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...

In recent years, the theory of Compressed Sensing has emerged as an alternative for the Shannon sampling theorem, suggesting that compressible signals can be reconstructed from far fewer samples than required by the Shannon sampling theorem. In fact the theory advocates that non-adaptive, ‘random’ functionals are in some sense optimal for this task. However, in practice, Compressed Sensing is v...

This article offers an accessible but rigorous and essentially self-contained account of some of the central ideas in compressed sensing, aimed at nonspecialists and undergraduates who have had linear algebra and some probability. The basic premise is first illustrated by considering the problem of detecting a few defective items in a large set. We then build up the mathematical framework of co...

Wideband spectrum sensing is one of the most challenging aspects of Cognitive Radio Networks (CRNs). It should be performed as fast and as accurate as possible. Traditional wideband spectrum sensing techniques require excessively high sampling rate analog-to-digital converters (ADCs). Compressed sensing was considered to enable wideband spectrum sensing at a much lower sampling rate below the N...

Compressed sensing is the theory and practice of subNyquist sampling of sparse signals of interest. Perfect reconstruction may then be possible with significantly fewer than the Nyquist required number of data. In this work, we consider a video system where acquisition is performed via framewise pure compressed sensing. The burden of quality video sequence reconstruction falls, then, solely on ...

Detection, Synchronization, Channel Estimation and Capacity in UWB Sensor Networks using Compressed Sensing by Shao-Yuan Chen Chair: Wayne E. Stark Conventional receivers in ultrawideband (UWB) communication system usually require high sampling rate and thus consume much power. With compressed sensing (CS), the sampling rate can potentially be reduced. In this thesis, the performance of CS used...

Undersampling k-space data is an efficient way to speed up the magnetic resonance imaging (MRI) process. As a newly developed mathematical framework of signal sampling and recovery, compressed sensing (CS) allows signal acquisition using fewer samples than what is specified by Nyquist-Shannon sampling theorem whenever the signal is sparse. As a result, CS has great potential in reducing data ac...