Related papers: Guaranteed sparse signal recovery with highly cohe…
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…
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 demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a "phase-only compressive sensing" (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover…
One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary…
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…
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…
This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible…
Recovering sparse signals from linear measurements has demonstrated outstanding utility in a vast variety of real-world applications. Compressive sensing is the topic that studies the associated raised questions for the possibility of a…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
Is it possible to detect a feature in an image without ever looking at it? Images are known to have sparser representation in Wavelets and other similar transforms. Compressed Sensing is a technique which proposes simultaneous acquisition…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, deep models can provide direct low-dimensional…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…
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…