Abstract The ${{\ell}}^{0} $ minimization of compressed sensing is often relaxed to
${{\ell}}^{1} $, which yields easy computation using the shrinkage mapping known as soft …

In many application areas ranging from bioinformatics to imaging, we are faced with the
following question: can we recover a sparse vector xo∈ ℝ N from its undersampled set of …

In the area of sparse recovery, numerous researches hint that non-convex penalties might
induce better sparsity than convex ones, but up until now those corresponding non-convex …

Compressed sensing (CS) states that a sparse signal can exactly be recovered from very
few linear measurements. While in many applications, real-world signals also exhibit …

Nonconvex ℓ p-minimization with p∈(0, 1) has been studied recently in the context of
compressed sensing. In this paper, we prove that as long as the sensing matrix A∈ R m× n …

The compressed sensing problem for redundant dictionaries aims to use a small number of
linear measurements to represent signals that are sparse with respect to a general …

An interesting topic in compressed sensing aims to recover signals with sparse
representations in a dictionary. Recently the performance of the ℓ 1-analysis method has …

Solving compressed sensing problems relies on the properties of sparse signals. It is
commonly assumed that the sparsity s needs to be less than one half of the spark of the …

Existing literatures suggest that sparsity is more likely to be induced with non-convex
penalties, but the corresponding algorithms usually suffer from multiple local minima. In this …

In many applications, we seek to recover signals from linear measurements far fewer than
the ambient dimension, given the signals have exploitable structures such as sparse vectors …