Related papers: Compressed Sensing with 1D Total Variation: Breaki…

Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…

We derive non-asymptotic bounds for the minimax risk of variable selection under expected Hamming loss in the Gaussian mean model in $\mathbb{R}^d$ for classes of $s$-sparse vectors separated from 0 by a constant $a > 0$. In some cases, we…

Compressed Sensing MRI reconstructs images of the body's internal anatomy from undersampled measurements, thereby reducing scan time. Recently, deep learning has shown great potential for reconstructing high-fidelity images from highly…

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…

From many fewer acquired measurements than suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that, a signal can be reconstructed with high probability when it exhibits sparsity in some domain. Most of…

We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a…

Compressive Sensing (CS) theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. Most of conventional CS recovery approaches, however,…

We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x in R^n from the signs of O(s log^2(n/s)) random linear measurements…

In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

We consider the recovery of sparse signals subject to sparse interference, as introduced in Studer et al., IEEE Trans. IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of…

This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…

This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present a proof of a result stated therein concerning the recovery…

Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to the entire frequency range. This…

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…

Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for…

Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…

This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, 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…

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…