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

Debashis Saikia; Bikash K. Behera; Mayukha Pal; Prasanta K. Panigrahi

quant-phApr 6, 2026

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

Authors: Debashis Saikia, Bikash K. Behera, Mayukha Pal, Prasanta K. Panigrahi

Organizations: Department of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram, India · Bikash’s Quantum (OPC) Pvt. Ltd., Mohanpur, WB, 741246 India · Università degli Studi di Cagliari, Via Is Mirrions, Cagliari, 09123, Italy · ABB Ability Innovation Center, Asea Brown Boveri Company, Hyderabad 500084, India ·

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 $γ$ 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.

Figures & tables

Fig. 1 : Proposed framework: intensity statistics are used to construct POVMs, followed by sharpening and probabilistic reconstruction.

Panel of Figure 2 — Fig. 2 : Original Images

Panel of Figure 3 — Fig. 3 : Comparison of reconstructed images obtained using Proposed K-Means, Proposed GMM, Unsharp Measurement, Multi-Otsu, and Fast Statistical Recursive methods (from left to right). Rows correspond to different datasets: (top to bottom) Lena, Peppers, Barbara, Image 100, and Image 1001.

Panel of Figure 4 — Fig. 4 : Comprehensive analysis of PSNR, SSIM, and $\%\Delta\mathrm{Entropy}$ with respect to $\gamma$ and $k$ for the proposed K-Means and GMM-based algorithms.

TABLE I : Performance comparison across multiple datasets.

Algorithm	PSNR	SSIM	$\Delta$ Entropy (%)
Gaussian Filter [ 25 ]	28.6607 $\pm$ 3.6590	0.8594 $\pm$ 0.0677	-1.1165 $\pm$ 1.3012
Bilateral Filter [ 26 ]	30.3301 $\pm$ 3.1104	0.8700 $\pm$ 0.0567	-1.1259 $\pm$ 1.1271
BM3D [ 27 ]	29.3568 $\pm$ 3.2318	0.8168 $\pm$ 0.0941	-1.4039 $\pm$ 1.3729
CLAHE [ 28 ]	20.2173 $\pm$ 2.1111	0.8373 $\pm$ 0.0438	6.4902 $\pm$ 4.5446
FastNLM [ 29 ]	34.7468 $\pm$ 2.2081	0.8911 $\pm$ 0.0634	-1.3443 $\pm$ 1.2013
Proposed (GMM)	33.4993 $\pm$ 1.9285	0.9483 $\pm$ 0.0208	-25.9031 $\pm$ 4.5221

TABLE II : Quantitative comparison on 100 randomly selected BSD500 images (mean

\pm

standard deviation). Proposed methods evaluated with

k=8

and

\gamma=2

as probabilistic intensity remapping models.

Panel of Figure 7 — Fig. 5 : Naimark dilation of the adaptive Gaussian POVM. A joint unitary $U$ acts on the system state $|I(x)\rangle$ and an ancilla initialized in $|0\rangle$ , producing the state $\sum_{k}(M_{k}|I(x)\rangle)\otimes|k\rangle$ . Measurement of the ancilla yields outcome $k$ with probability $p_{k}(x)=\mathrm{Tr}(E_{k}\rho_{x})$ .

Panel of Figure 8 — Fig. 6 : Robustness of the proposed model with K-means clustering. The first four images show reconstructed outputs for varying $k$ , and the last image is the original.

Panel of Figure 9 — Fig. 7 : Robustness of the proposed model with Gaussian Mixture model clustering. The first four images show reconstructed outputs for varying $k$ , and the last image is the original.

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