A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
SIAM Journal on Scientific Computing
Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem
SIAM Journal on Matrix Analysis and Applications
Blind Deconvolution Using a Regularized Structured Total Least Norm Algorithm
SIAM Journal on Matrix Analysis and Applications
A Note on Antireflective Boundary Conditions and Fast Deblurring Models
SIAM Journal on Scientific Computing
A Global Solution for the Structured Total Least Squares Problem with Block Circulant Matrices
SIAM Journal on Matrix Analysis and Applications
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
Overview of total least-squares methods
Signal Processing
Deblurring Methods Using Antireflective Boundary Conditions
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
Antireflective boundary conditions for deblurring problems
Journal of Electrical and Computer Engineering - Special issue on iterative signal processing in communications
The constrained total least squares technique and its applicationsto harmonic superresolution
IEEE Transactions on Signal Processing
Formulation and solution of structured total least norm problemsfor parameter estimation
IEEE Transactions on Signal Processing
Regularized constrained total least squares image restoration
IEEE Transactions on Image Processing
| Hi-index | 7.29 |
The problem of reconstructing signals and images from degraded ones is considered in this paper. The latter problem is formulated as a linear system whose coefficient matrix models the unknown point spread function and the right hand side represents the observed image. Moreover, the coefficient matrix is very ill-conditioned, requiring an additional regularization term. Different boundary conditions can be proposed. In this paper antireflective boundary conditions are considered. Since both sides of the linear system have uncertainties and the coefficient matrix is highly structured, the Regularized Structured Total Least Squares approach seems to be the more appropriate one to compute an approximation of the true signal/image. With the latter approach the original problem is formulated as an highly nonconvex one, and seldom can the global minimum be computed. It is shown that Regularized Structured Total Least Squares problems for antireflective boundary conditions can be decomposed into single variable subproblems by a discrete sine transform. Such subproblems are then transformed into one-dimensional unimodal real-valued minimization problems which can be solved globally. Some numerical examples show the effectiveness of the proposed approach.