Related papers: Sequential adaptive compressed sampling via Huffma…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
In this paper, we propose \textit{coded compressive sensing} that recovers an $n$-dimensional integer sparse signal vector from a noisy and quantized measurement vector whose dimension $m$ is far-fewer than $n$. The core idea of coded…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
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 refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals 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…
There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach starts with a geometric constraint on the measurement matrix and then uses linear programming to decode information…
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long…
A new line of research uses compression methods to measure the similarity between signals. Two signals are considered similar if one can be compressed significantly when the information of the other is known. The existing compression-based…
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…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
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 relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this…
Compressive sensing is considered a huge breakthrough in signal acquisition. It allows recording an image consisting of $N^2$ pixels using much fewer than $N^2$ measurements if it can be transformed to a basis where most pixels take on…