Iterative exact global histogram specification and SSIM gradient ascent: a proof of convergence, step size and parameter selection

TL;DR

This paper proves the convergence of an iterative method combining SSIM gradient ascent and exact global histogram specification, providing insights into step size and parameter selection for optimizing image quality.

Contribution

It introduces a convergence proof for the SSIM-optimized EGHS method and discusses optimal parameter and step size selection.

Findings

Convergence is guaranteed with small step sizes.

The method improves structural similarity in iterative steps.

Guidelines for parameter selection are provided.

Abstract

The SSIM-optimized exact global histogram specification (EGHS) is shown to converge in the sense that the first order approximation of the result's quality (i.e., its structural similarity with input) does not decrease in an iteration, when the step size is small. Each iteration is composed of SSIM gradient ascent and basic EGHS with the specified target histogram. Selection of step size and other parameters is also discussed.