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From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…
In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem…
Compressed sensing is a signal processing scheme that reconstructs high-dimensional sparse signals from a limited number of observations. In recent years, various problems involving signals with a finite number of discrete values have been…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…
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…
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes…
The Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization, as is exemplified by the so-called one-bit compressed sensing framework which aims to recover a signal from…
Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are…
For wideband spectrum sensing, compressive sensing has been proposed as a solution to speed up the high dimensional signals sensing and reduce the computational complexity. Compressive sensing consists of acquiring the essential information…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
Finite-rate-of-innovation (FRI) signals are ubiquitous in applications such as radar, ultrasound, and time of flight imaging. Due to their finite degrees of freedom, FRI signals can be sampled at sub-Nyquist rates using appropriate sampling…
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
We consider the problem of recovering a single or multiple frequency-sparse signals, which share the same frequency components, from a subset of regularly spaced samples. The problem is referred to as continuous compressed sensing (CCS) in…
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…
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…