Derivative-free MLSCD conjugate gradient method for sparse signal and image reconstruction in compressive sensing

Gradient-based compressive sensing for noise image and video reconstruction

In this study, a fast gradient-based compressive sensing (FGB-CS) for noise image and video is proposed. Given a noise image or video, the authors first make it sparse by orthogonal transformation, and then reconstruct it by solving a convex optimisation problem with a novel gradient-based method. The main contribution is twofold. Firstly, they deal with the noise signal reconstruction as a con...

Compressive Sensing Reconstruction for Sparse 2D Data

In this paper we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly under-sampled data is proposed. It is based on the analytically determined threshold that precisely separates signal and non-signal components in the 2D DFT domain. The algorithm operates fast in a single iteration providing the accurate si...

Preconditioned Conjugate Gradient Method for Boundary Artifact-Free Image Deblurring

Several methods have been proposed to reduce boundary artifacts in image deblurring. Some of those methods impose certain assumptions on image pixels outside the field-of-view; the most important of these assume reflective or anti-reflective boundary conditions. Boundary condition methods, including reflective and anti-reflective ones, however, often fail to reduce boundary artifacts, and, in s...

Compressive Sensing of Sparse Signals in the Hermite Transform Basis: Analysis and Algorithm for Signal Reconstruction

—An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the probability of success in detection of signal components support is determined. Based on the probabilistic analysis, a threshold for the detection of signal compo...

Spatial Compressive Sensing for Strain Data Reconstruction from Sparse Sensors