相关论文: Optimization for Compressed Sensing: the Simplex M…
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
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…
We first propose a novel criterion that guarantees that an $s$-sparse signal is the local minimizer of the $\ell_1/\ell_2$ objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition…
Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt…
Tensor Compressive Sensing (TCS) is a multidimensional framework of Compressive Sensing (CS), and it is advantageous in terms of reducing the amount of storage, easing hardware implementations and preserving multidimensional structures of…
The bound that arises out of sparse recovery analysis in compressed sensing involves input signal sparsity and some property of the sensing matrix. An effort has therefore been made in the literature to optimize sensing matrices for optimal…
One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to…
In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage…
Compressed sensing is a processing method that significantly reduces the number of measurements needed to accurately resolve signals in many fields of science and engineering. We develop a two-dimensional (2D) variant of compressed sensing…
Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to…
Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the…
Recently, significant connections between compressed sensing problems and optimization of a particular class of functions relating to solutions of Hamilton-Jacobi equation was discovered. In this paper we introduce a fast approximate…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…
One-bit compressed sensing (1bCS) is an extreme-quantized signal acquisition method that has been intermittently studied in the past decade. In 1bCS, linear samples of a high dimensional signal are quantized to only one bit per sample (sign…
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…