Related papers: Compressive Measurements Generated by Structurally…
Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
We propose a novel sparsity model for distributed compressed sensing in the multiple measurement vectors (MMV) setting. Our model extends the concept of row-sparsity to allow more general types of structured sparsity arising in a variety of…
We use an agnostic information-theoretic approach to investigate the statistical properties of natural images. We introduce the Multiscale Relevance (MSR) measure to assess the robustness of images to compression at all scales. Starting in…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
Exploiting intrinsic structures in sparse signals underpins the recent progress in compressive sensing (CS). The key for exploiting such structures is to achieve two desirable properties: generality (\ie, the ability to fit a wide range of…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…
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 revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random. These matrices have a one-to-one correspondence with the adjacency…
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,…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
Compressed sensing is an imaging paradigm that allows one to invert an underdetermined linear system by imposing the a priori knowledge that the sought after solution is sparse (i.e., mostly zeros). Previous works have shown that if one…
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…
In this paper, we consider a situation where a decision maker's (DM's) risk preference can be described by a spectral risk measure (SRM) but there is not a single SRM which can be used to represent the DM's preferences consistently.…
In the present note we develop some theoretical results in the theory of anisotropic compressed sensing that allow to take structured sparsity and variable density structured sampling into account. We expect that the obtained results will…
In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…
Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…
This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…