A null-space-based weightedl1minimization approach to compressed sensing

A null space property approach to compressed sensing with frames

An interesting topic in compressive sensing concerns problems of sensing and recovering signals with sparse representations in a dictionary. In this note, we study conditions of sensing matrices A for the `-synthesis method to accurately recover sparse, or nearly sparse signals in a given dictionary D. In particular, we propose a dictionary based null space property (D-NSP) which, to the best o...

A Null-Space-Based Weighted `1 Minimization Approach to Compressed Sensing∗

It has become an established fact that the constrained `1 minimization is capable of recovering the sparse solution from a small number of linear observations and the reweighted version can significantly improve its numerical performance. The recoverability is closely related to the Restricted Isometry Constant (RIC) of order s (s is an integer), often denoted as δs. A class of sufficient condi...

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...

A null space analysis of the L1 synthesis method in dictionary-based compressed sensing

An interesting topic in compressed sensing aims to recover signals with sparse representations in a dictionary. Recently the performance of the l1-analysis method has been a focus, while some fundamental problems for the l1-synthesis method are still unsolved. For example, what are the conditions for it to stably recover compressible signals under noise? Whether coherent dictionaries allow the ...

A Compressed Sensing Approach to Observing