Related papers: Compressed sensing with combinatorial designs: the…
Construction on the measurement matrix $A$ is a central problem in compressed sensing. Although using random matrices is proven optimal and successful in both theory and applications. A deterministic construction on the measurement matrix…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…
This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…
Compressed sensing is the art of reconstructing structured $n$-dimensional vectors from substantially fewer measurements than naively anticipated. A plethora of analytic reconstruction guarantees support this credo. The strongest among them…
Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing…
For any rational number $h$ and all sufficiently large $n$ we give a deterministic construction for an $n\times \lfloor hn\rfloor$ compressed sensing matrix with $(\ell_1,t)$-recoverability where $t=O(\sqrt{n})$. Our method uses pairwise…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…
Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications,…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted…
A combinatorial approach to compressive sensing based on a deterministic column replacement technique is proposed. Informally, it takes as input a pattern matrix and ingredient measurement matrices, and results in a larger measurement…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
The class of Fourier matrices is of special importance in compressed sensing (CS). This paper concerns deterministic construction of compressed sensing matrices from Fourier matrices. By using Katz' character sum estimation, we are able to…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representation. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be…