A Fast Algorithm for Image Deconvolution Based on a Rank Constrained Inverse Matrix Approximation Problem

2021 ◽  
pp. 165-176
Author(s):  
Pablo Soto-Quiros ◽  
Juan Jose Fallas-Monge ◽  
Jeffry Chavarría-Molina
Keyword(s):  
Fast Algorithm ◽  
Approximation Problem ◽  
Inverse Matrix ◽  
Image Deconvolution ◽  
Matrix Approximation

scholarly journals The core inverse and constrained matrix approximation problem

2020 ◽  
Vol 18 (1) ◽  
pp. 653-661 ◽  
Author(s):  
Hongxing Wang ◽  
Xiaoyan Zhang
Keyword(s):  
Unique Solution ◽  
Approximation Problem ◽  
Frobenius Norm ◽  
Matrix Approximation ◽  
The Core ◽  
Core Inverse

Abstract In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse: ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M), where M\in {{\mathbb{C}}}_{n}^{\text{CM}} . We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.

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