Iterative Alpha Expansion for Estimating Gradient-Sparse Signals from Linear Measurements

A Fast Iterative Algorithm for Recovery of Sparse Signals from One-Bit Quantized Measurements

This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal recovery. Also, in the proposed method, sigmoid functions are introduced to quantify the consistency between the acquired one-bit quantized data and the recon...

Sparse Signal Recovery from Nonadaptive Linear Measurements

The theory of Compressed Sensing , the emerging sampling paradigm ‘that goes against the common wisdom’ , asserts that ‘one can recover signals in R from far fewer samples or measurements , if the signal has a sparse representation in some orthonormal basis, from m ≈ O(klogn), k ≪ n nonadaptive measurements . The accuracy of the recovered signal is as good as that attainable with direct knowled...

Iterative methods for sparse linear systems

Linear System Solvers : Sparse Iterative

In this chapter we will present an overview of a number of related iterative methods for the solution of linear systems of equations. These methods are so-called Krylov projection type methods and they include popular methods as Conjugate Gradients, Bi-Conjugate Gradients, LSQR and GMRES. We will sketch how these methods can be derived from simple basic iteration formulas, and how they are inte...

Recovery of Clustered Sparse Signals from Compressive Measurements

We introduce a new signal model, called (K,C)-sparse, to capture K-sparse signals in N dimensions whose nonzero coefficients are contained within at most C clusters, with C < K ≪ N . In contrast to the existing work in the sparse approximation and compressive sensing literature on block sparsity, no prior knowledge of the locations and sizes of the clusters is assumed. We prove that O (K + C lo...