Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images

TL;DR

This paper introduces two convex sets based on phase and total variation for blind deconvolution of microscopic images, improving image restoration by leveraging symmetry and adaptive TV constraints.

Contribution

It proposes novel convex sets for blind deconvolution that utilize phase information and adaptive TV constraints, enhancing existing algorithms.

Findings

Convex sets based on FT phase improve deblurring accuracy.

Adaptive TV set eliminates need for predefined bounds.

Simulation results demonstrate effectiveness of the proposed sets.

Abstract

In this article, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the epigraph set of Total Variation (TV) function. This set does not need a prescribed upper bound on the total variation of the image. The upper bound is automatically adjusted according to the current image of the restoration process. Both of these two closed and convex sets can be used as a part of any blind deconvolution algorithm. Simulation examples are presented.