相关论文: Efficient and Robust Compressed Sensing using High…
We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal…
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples.…
The rapid developing area of compressed sensing suggests that a sparse vector lying in an arbitrary high dimensional space can be accurately recovered from only a small set of non-adaptive linear measurements. Under appropriate conditions…
Data processing has to deal with many practical difficulties. Data is often corrupted by artifacts or noise and acquiring data can be expensive and difficult. Thus, the given data is often incomplete and inaccurate. To overcome these…
Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…
Heat diffusion processes have found wide applications in modelling dynamical systems over graphs. In this paper, we consider the recovery of a $k$-bandlimited graph signal that is an initial signal of a heat diffusion process from its…
Though the method of least squares has been used for a long time in solving signal processing problems, in the recent field of sparse recovery from compressed measurements, this method has not been given much attention. In this paper we…
We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…
This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key…
We introduce a new ensemble of random bipartite graphs, which we term the `smearing ensemble', where each left node is connected to some number of consecutive right nodes. Such graphs arise naturally in the recovery of sparse wavelet…
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occuring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and we show…
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…
A natural requirement of many distributed structures is fault-tolerance: after some failures, whatever remains from the structure should still be effective for whatever remains from the network. In this paper we examine spanners of general…
Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
In this paper, we study the sample complexity and develop efficient optimal algorithms for 1-bit phase retrieval: recovering a signal $\mathbf{x}\in\mathbb{R}^n$ from $m$ phaseless bits…
Compressive sensing has been used to demonstrate scene reconstruction and source localization in a wide variety of devices. To date, optical compressive sensors have not been able to achieve significant volume reduction relative to…
The problem of detecting the sparsity pattern of a k-sparse vector in R^n from m random noisy measurements is of interest in many areas such as system identification, denoising, pattern recognition, and compressed sensing. This paper…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…