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

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.