The theory of compressed sensing (CS) shows that signals can be acquired at sub-Nyquist rates if they are sufficiently sparse or compressible. Since many images bear this property, several acquisition models have been proposed for optical CS. An interesting approach is random convolution (RC). In contrast with single-pixel CS approaches, RC allows for the parallel capture of visual information ...

This paper discusses the theory for RIPless in compressed sensing (CS). In the literature, E.J. Candès has proved that δ2s < √ 2 − 1 is a sufficient condition via l1 optimization having s-sparse vector solution. Later, many researchers have improved the sufficient conditions on δ2s or δs. Such researches have supposed that a matrix A obeys RIP and a signal to recover is sparse. In this paper, w...

Conventional speech scramblers have three disadvantages, including heavy communication overhead, signal features underexploitation, and low attack resistance. In this study, we propose a scrambling-based speech encryption scheme via compressed sensing (CS). Distinguished from conventional scramblers, the above problems are solved in a unified framework by utilizing the advantages of CS. The pre...

We consider the conjectured O(N2+ ) time complexity of multiplying any two N × N matrices A and B. Our main result is a deterministic Compressed Sensing (CS) algorithm that both rapidly and accurately computes A · B provided that the resulting matrix product is sparse/compressible. As a consequence of our main result we increase the class of matrices A, for any given N × N matrix B, which allow...

We investigate the Direction of Arrival (DoA) estimation for smalland large-scale antenna arrays with a small and a large number of antenna elements, respectively. Two classes of algorithms are considered, namely subspaceand compressed sensing (CS)-based algorithms. We compare those algorithms in terms of both the DoA estimation performance and the computational complexity based on different pa...

7 processing. Conventional dimensionality reduction on-board remote devices is 8 often prohibitive due to limited computational resources; on the other hand, 9 integrating random projections directly into signal acquisition offers an alternative 10 to explicit dimensionality reduction without incurring sender-side computational 11 cost. Receiver-side reconstruction of hyperspectral data from su...

Compressive sensing (CS) exploits the sparsity of the commonly encountered signals and provides the data compression at the first step of the image acquisition. In this paper, performance of various wavelet based CS techniques has been analysed. It is based on the concept that small collections of non-adaptive linear projections of a sparse signal contain enough information for its effective re...

Compressed sensing (CS) has recently emerged as a powerful signal acquisition paradigm. CS enables the recovery of high-dimensional sparse signals from much fewer samples than usually required. Further, quite a few recent channel measurement experiments show that many wireless channels also tend to exhibit sparsity. In this case, CS theory can be applicable to sparse channel estimation and its ...

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via l1-l1 and l1-l2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruc...