Non-local image deconvolution by Cauchy sequence

TL;DR

This paper introduces a novel non-local image deconvolution method based on Cauchy sequences and Taylor series expansion, resulting in a faster algorithm with improved theoretical accuracy over traditional methods.

Contribution

It develops a new deconvolution approach using Cauchy sequences and Taylor series, offering a more precise and efficient iterative algorithm for image deblurring.

Findings

Deconvolution converges faster than Richardson-Lucy.

The method achieves higher accuracy in image restoration.

The approach is grounded in continuous function space optimization.

Abstract

We present the deconvolution between two smooth function vectors as a Cauchy sequence of weight functions. From this we develop a Taylor series expansion of the convolution problem that leads to a non-local approximation for the deconvolution in terms of continuous function spaces. Optimisation of this form against a given measure of error produces a theoretically more exact algorithm. The discretization of this formulation provides a deconvolution iteration that deconvolves images quicker than the Richardson-Lucy algorithm.