An Alternating $l_1$ Approach to the Compressed Sensing Problem

An Alternating l1 Approach to the Compressed Sensing Problem

Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution of an underdetermined system of linear equations with the smallest possible support. The most studied relaxation of this hard combinatorial problem is the l1-...

A Block-Wise random sampling approach: Compressed sensing problem

The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...

The Two Stage l1 Approach to the Compressed Sensing Problem

This paper gives new results on the recovery of sparse signals using l1-norm minimization. We introduce a two-stage l1 algorithm equivalent to the first two iterations of the alternating l1 relaxation introduced in [5] for an appropriate value of the Lagrange multiplier. The first step consists of the standard l1 relaxation. The second step consists of optimizing the l1 norm of a subvector whos...

a block-wise random sampling approach: compressed sensing problem

the focus of this paper is to consider the compressed sensing problem. it is stated that the compressed sensing theory, under certain conditions, helps relax the nyquist sampling theory and takes smaller samples. one of the important tasks in this theory is to carefully design measurement matrix (sampling operator). most existing methods in the literature attempt to optimize a randomly initiali...

An Introduction to Compressed Sensing