Related papers: Restricted Isometries for Partial Random Circulant…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
The many variants of the restricted isometry property (RIP) have proven to be crucial theoretical tools in the fields of compressed sensing and matrix completion. The study of extending compressed sensing to accommodate phaseless…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the…
Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand and Staneva shown in \cite{CS1} that the $l_p$ minimization with $0<p<1$ recovers…
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…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an $s$-sparse signal from linear measurements…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
Compressed Sensing (CS) is an emerging field that enables reconstruction of a sparse signal $x \in {\mathbb R} ^n$ that has only $k \ll n$ non-zero coefficients from a small number $m \ll n$ of linear projections. The projections are…
Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…
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…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
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…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…