Unsharp Measurement with Adaptive Gaussian POVMs for Quantum-Inspired Image Processing

TL;DR

This paper introduces a data-adaptive, probabilistic intensity remapping framework for grayscale images that preserves structure and offers smooth control over smoothing versus discrimination, outperforming traditional histogram-based methods.

Contribution

It presents a novel continuous, data-driven remapping approach using Gaussian components and a nonlinear sharpening parameter for enhanced image structure preservation.

Findings

Better structural fidelity than thresholding-based methods

Controlled information reduction via entropy measures

Improved PSNR and SSIM on benchmark images

Abstract

We propose a data-adaptive probabilistic intensity remapping framework for structure-preserving transformation of grayscale images. The suggested method formulates intensity transformation as a continuous, data-driven remapping process, in contrast to traditional histogram-based techniques that rely on hard thresholding and generate piecewise-constant mappings. The image statistics yield representative intensity values, and Gaussian-based weighting methods probabilistically allocate each pixel to several components. Smooth transitions while preserving structural features are achieved by computing the output intensity as an expectation over these components. A smooth transition from soft probabilistic remapping to hard assignment is made possible by the introduction of a nonlinear sharpening parameter $\gamma$ to regulate the degree of localization. This offers clear control over the trade-off between intensity discrimination and smoothing. Furthermore, the resolution of the remapping function is determined by the number of components $k$. When compared to thresholding-based methods, experimental results on standard benchmark images show that the suggested method achieves better structural fidelity and controlled information reduction as measured by PSNR, SSIM, and entropy. Overall, by allowing continuous, probabilistic intensity modifications, the framework provides a robust and efficient substitute for discrete thresholding.