An Extended Reweighted ℓ1 Minimization Algorithm for Image Restoration

This paper proposes an effective extended reweighted ℓ1 minimization algorithm (ERMA) to solve the basis pursuit problem minu∈Rnu1:Au=f in compressed sensing, where A∈Rm×n, m≪n. The fast algorithm is based on linearized Bregman iteration with soft thresholding operator and generalized inverse iteration. At the same time, it also combines the iterative reweighted strategy that is used to solve minu∈Rnupp:Au=f problem, with the weight ωiu,p=ε+ui2p/2−1. Numerical experiments show that this l1 minimization persistently performs better than other methods. Especially when p=0, the restored signal by the algorithm has the highest signal to noise ratio. Additionally, this approach has no effect on workload or calculation time when matrix A is ill-conditioned.

Artifact removal in the contour areas of SAXS-CT images by Tikhonov-L1 minimization

Small-angle X-ray scattering (SAXS) coupled with computed tomography (CT), denoted SAXS-CT, has enabled the spatial distribution of the characteristic parameters (e.g. size, shape, surface, length) of nanoscale structures inside samples to be visualized. In this work, a new scheme with Tikhonov regularization was developed to remove the effects of artifacts caused by streak scattering originating from the reflection of the incident beam in the contour regions of the sample. The noise due to streak scattering was successfully removed from the sinogram image and hence the CT image could be reconstructed free from artifacts in the contour regions.

A Neurodynamic Optimization Approach for L1 Minimization with Application to Compressed Image Reconstruction

This paper presents a neurodynamic optimization approach for l1 minimization based on an augmented Lagrangian function. By using the threshold function in locally competitive algorithm (LCA), subgradient at a nondifferential point is equivalently replaced with the difference of the neuronal state and its mapping. The efficacy of the proposed approach is substantiated by reconstructing three compressed images.

Weighted lp − l1 minimization methods for block sparse recovery and rank minimization

This paper considers block sparse recovery and rank minimization problems from incomplete linear measurements. We study the weighted [Formula: see text] [Formula: see text] norms as a nonconvex metric for recovering block sparse signals and low-rank matrices. Based on the block [Formula: see text]-restricted isometry property (abbreviated as block [Formula: see text]-RIP) and matrix [Formula: see text]-RIP, we prove that the weighted [Formula: see text] minimization can guarantee the exact recovery for block sparse signals and low-rank matrices. We also give the stable recovery results for approximately block sparse signals and approximately low-rank matrices in noisy measurements cases. Our results give the theoretical support for block sparse recovery and rank minimization problems.