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

2026-04-06

AI Summary

This work proposes a novel quantum-inspired approach to image processing by introducing unsharp quantum measurements and adaptive Gaussian positive operator-valued measures (POVMs). Unlike conventional methods that rely on segmentation or thresholding and struggle to balance structural preservation with adaptive probabilistic transformation, the proposed framework embeds pixel intensities into a finite-dimensional Hilbert space. It constructs data-adaptive POVM operators based on a histogram Gaussian mixture model and incorporates a nonlinear sharpening parameter γ along with the number of Gaussian centers k to modulate the locality and resolution of the measurement process, thereby enabling a continuous transition from probabilistic smoothing to projective measurement. Experimental results on standard test images demonstrate that the method effectively achieves a balance between preserving structural information and performing adaptive grayscale transformation.

Abstract

We propose a quantum measurement-based framework for probabilistic transformation of grayscale images using adaptive positive operator-valued measures (POVMs). In contrast, to existing approaches that are largely centered around segmentation or thresholding, the transformation is formulated here as a measurement-induced process acting directly on pixel intensities. The intensity values are embedded in a finite-dimensional Hilbert space, which allows the construction of data-adaptive measurement operators derived from Gaussian models of the image histogram. These operators naturally define an unsharp measurement of the intensity observable, with the reconstructed image obtained through expectation values of the measurement outcomes. To control the degree of measurement localization, we introduce a nonlinear sharpening transformation with a sharpening parameter, $γ$, that induces a continuous transition from unsharp measurements to projective measurements. This transition reflects an inherent trade-off between probabilistic smoothing and localization of intensity structures. In addition to the nonlinear sharpening parameter, we introduce another parameter $k$ (number of gaussian centers) which controls the resolution of the image during the transformation. Experimental results on standard benchmark images show that the proposed method gives effective data-adaptive transformations while preserving structural information.

Problem

• unsharp measurement
• adaptive Gaussian POVMs
• quantum-inspired image processing
• intensity transformation
• probabilistic smoothing

Innovation

• adaptive POVMs
• unsharp measurement
• quantum-inspired image processing
• nonlinear sharpening
• Gaussian histogram modeling