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 · Center for Quantum Science and Technology, Siksha O Anusandhan University, Bhubaneswar, India · Department of Physical Sciences, Indian Institute of Science Education and Research (IISER), Kolkata, Mohanpur 741246, West Bengal, India
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.
Fig. 2 : Original Images
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.
Fig. 4 : Comprehensive analysis of PSNR, SSIM, and %ΔEntropy with respect to γ and k for the proposed K-Means and GMM-based algorithms.
TABLE I : Performance comparison across multiple datasets.
Algorithm
PSNR
SSIM
Δ Entropy (%)
Gaussian Filter [ 25 ]
28.6607 ± 3.6590
0.8594 ± 0.0677
-1.1165 ± 1.3012
Bilateral Filter [ 26 ]
30.3301 ± 3.1104
0.8700 ± 0.0567
-1.1259 ± 1.1271
BM3D [ 27 ]
29.3568 ± 3.2318
0.8168 ± 0.0941
-1.4039 ± 1.3729
CLAHE [ 28 ]
20.2173 ± 2.1111
0.8373 ± 0.0438
6.4902 ± 4.5446
FastNLM [ 29 ]
34.7468 ± 2.2081
0.8911 ± 0.0634
-1.3443 ± 1.2013
Proposed (GMM)
33.4993 ± 1.9285
0.9483 ± 0.0208
-25.9031 ± 4.5221
TABLE II : Quantitative comparison on 100 randomly selected BSD500 images (mean ± standard deviation). Proposed methods evaluated with k=8 and γ=2 as probabilistic intensity remapping models.
Fig. 5 : Naimark dilation of the adaptive Gaussian POVM. A joint unitary U acts on the system state ∣I(x)⟩ and an ancilla initialized in ∣0⟩ , producing the state ∑k(Mk∣I(x)⟩)⊗∣k⟩ . Measurement of the ancilla yields outcome k with probability pk(x)=Tr(Ekρx) .
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.
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.
The quantum nature of light determines the inherent Poisson stochasticity of photon detection, which is ubiquitous in photography, microscopy, and astronomy. However, our controlled numerical studies reveal that the signal-dependency, heteroscedasticity, and statistical asymmetry of Poisson-mixed noise make it challenging for existing denoisers to learn. In contrast, i.i.d. Gaussian noise, with its statistical independence and symmetric distribution, is easier to model for networks. To address this gap, we propose Poisson2Gaussian (P2G), a noise Gaussianization method that explicitly converts complex real-world noise to i.i.d. Gaussian noise via probability density matching beyond low-order moments. We also design an unbiased denoising framework that synergizes P2G with downstream denoisers, ensuring convergence to the underlying signal without requiring paired clean data or explicit noise parameters. Extensive experiments demonstrate that P2G consistently achieves state-of-the-art performance across diverse datasets. In challenging scenarios where noise strongly deviates from Gaussian statistics, our method improves the PSNR by up to 0.75 dB. Notably, P2G is architecture-agnostic and can provide universal improvements for various denoisers. The source code will be publicly available.
Xirou Zhou, Zijing Xu, Yibo Qu +3
College of AI, Tsinghua University, Beijing, China · Department of Automation, Tsinghua University, Beijing, China · School of Electronic and Information Engineering, Beihang University, Beijing, China
2D Gaussian Splatting is an attractive direction for image representation due to its explicit formulation, fast rasterization, and favorable decoding efficiency. The representation quality of this paradigm depends on the proper allocation of Gaussian capacity to the demanding regions. However, existing methods fail to allocate Gaussian capacity efficiently during optimization: under-reconstructed content is often refined in a fragmented pixel-wise manner, while neighboring optimized Gaussians with similar attributes are redundantly retained. This inefficiency motivates the need for a density control framework that jointly addresses insufficient allocation in under-reconstructed regions and redundant allocation in over-reconstructed regions. Our key insight is that this framework should exploit two complementary forms of locality: the local continuity of reconstruction errors in image space for improved Gaussian allocation, and the local similarity of neighboring Gaussians in Gaussian space for redundant elimination. Based on this insight, we propose Locality-Aware Density Control (LocoADC), a plug-and-play framework that improves Gaussian capacity utilization through Region-wise Gaussian Densification (RGD) and Similarity-Driven Gaussian Merging (SDGM) strategies, together with a local color consistency constraint for more reliable merging. Extensive experiments on diverse datasets show that LocoADC consistently improves multiple baselines by enabling more effective local Gaussian allocation, including a 2.93 dB PSNR gain over GI on the CLIC dataset under the same 30k Gaussian budget. Code is available at: https://github.com/ChenJiaCong-1005/LocoADC.
Jiacong Chen, Qingyu Mao, Xiandong Meng +5
Shenzhen University Shenzhen, China · Pengcheng Laboratory Shenzhen, China · Harbin Institute of Technology (Shenzhen) Shenzhen, China
Implicit Neural Representations (INRs) approximate discrete data through continuous functions and are commonly used for encoding 2D images. Traditional image-based INRs employ neural networks to map pixel coordinates to RGB values, capturing shapes, colors, and textures within the network's weights. Recently, GaussianImage has been proposed as an alternative, using Gaussian functions instead of neural networks to achieve comparable quality and compression. Such a solution obtains a quality and compression ratio similar to classical INR models but does not allow image modification. In contrast, our work introduces a novel method, MiraGe, which uses mirror reflections to perceive 2D images in 3D space and employs flat-controlled Gaussians for precise 2D image editing. Our approach improves the rendering quality and allows realistic image modifications, including human-inspired perception of photos in the 3D world. Thanks to modeling images in 3D space, we obtain the illusion of 3D-based modification in 2D images. We also show that our Gaussian representation can be easily combined with a physics engine to produce physics-based modification of 2D images. Consequently, MiraGe allows for better quality than the standard approach and natural modification of 2D images
Joanna Waczyńska, Tomasz Szczepanik, Piotr Borycki +3
1Jagiellonian University · University of Cambridge