Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2505.21546

Image denoising as a conditional expectation

Sajal Chakroborty·Suddhasattwa Das
View original source ↗Read source document ↗Export metadata ↓

Abstract

All techniques for denoising involve a notion of a true (noise-free) image, and a hypothesis space. The hypothesis space may reconstruct the image directly as a grayscale valued function, or indirectly by its Fourier or wavelet spectrum. Most common techniques estimate the true image as a projection to some subspace. We propose an interpretation of a noisy image as a collection of samples drawn from a certain probability space. Within this interpretation, projection based approaches are not guaranteed to be unbiased and convergent. We present a data-driven denoising method in which the true image is recovered as a conditional expectation. Although the probability space is unknown apriori, integrals on this space can be estimated by kernel integral operators. The true image is reformulated as the least squares solution to a linear equation in a reproducing kernel Hilbert space (RKHS), and involving various kernel integral operators as linear transforms. Assuming the true image to be a continuous function on a compact planar domain, the technique is shown to be convergent as the number of pixels goes to infinity. We also show that for a picture with finite number of pixels, the convergence result can be used to choose the various parameters for an optimum denoising result.

Explore related subjects

eess.IVcs.CVmath.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sajal Chakroborty, Suddhasattwa Das. 2025-05-24. Image denoising as a conditional expectation. https://arxiv.org/abs/2505.21546

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

LaminoDiff: Generative Computed Laminography via Near-Isotropic Spectral Supervision and Anisotropic Geometry

Computed Laminography (CL) is widely used for nondestructive inspection of extended planar objects, but its restricted angular coverage produces an anisotropic point spread function, missing-cone spectral incompleteness, and severe aliasing with interlayer leakage. This paper presents LaminoDiff, a physics-constrained diffusion framework for CL reconstruction. During training, a CT-derived near-isotropic supervision target is reconstructed from full-angle Computed Tomography (CT) projections physically degraded to match CL detector noise and focal-spot blur while retaining full angular coverage; it is withheld from inference. At inference, the reverse process uses only the CL observation. An Anisotropic Representation (AR) constructs depth-aware channels from three adjacent slices: a neighbor average, a center-neighbor residual, and the retained current slice, followed by directional in-plane feature extraction. Experiments on simulated and real multilayer printed circuit board data, including ball grid array and high-frequency stub samples, show that LaminoDiff improves artifact suppression, edge preservation, and depth stratification over analytic Feldkamp--Davis--Kress and representative learning-based baselines.

eess.IV↗
arXiv2026

IViT: A Novel Interpretable Visual Transformer for Skin Disease Detection

The clinical diagnosis of skin diseases is susceptible to interference from inter-class similarity of skin lesions, and over-reliance on clinicians'experience easily leads to subjective bias. Although existing deep learning aided diagnosis methods achieve competitive accuracy, they suffer from the black-box opacity of Vision Transformer (ViT) and poor adaptability to medical few-shot scenarios. Moreover, mainstream explainable algorithms generally face the bottleneck of significant accuracy degradation when improving interpretability. This paper proposes an interpretable ViT (IViT) constrained by Quadratic Programming (QP). The introduced pre-trained transfer learning adapts to few-shot feature extraction. A discrete QP feature selection framework is constructed to screen generic and discriminative features consistent with clinical diagnostic logic. A multi-objective loss function is designed to reduce feature redundancy and optimize activation distribution while preserving classification performance. Experimental results on six standard skin disease datasets show that IViT achieves an accuracy of 93.80%, only 0.21% lower than the baseline, with feature redundancy reduced by 29.5%. Its core activation regions are consistent with clinically concerned lesion areas. The proposed model balances accuracy and interpretability, providing a reliable solution for the clinical deployment of few-shot intelligent skin disease diagnosis.

eess.IV↗
arXiv2026

Automated Distinction of Intimal and Medial Intracranial Arterial Calcification from CT Head

Intracranial arterial calcifications (IACs) are a common finding on clinical non-contrast enhanced head CT scans and are associated with neurovascular disease. Calcifications can occur in the intimal or medial layer of the arterial wall, subtypes that differ in aetiology and may have distinct clinical relevance. These subtypes can be visually distinguished by radiologists based on the shape of the calcifications. We investigate three automated approaches for subtype classification of IAC from head CT-derived segmentation masks: (1) an automated adaptation of the established radiological visual score, (2) a sphericity-based method, and (3) a method based on shape embeddings extracted by a medical shape foundation model. All approaches use the same lightweight classification pipeline on top of the features they compute and are evaluated using 5-fold cross-validation. The three methods achieved comparable performance, with the embedding-based approach yielding the best overall results with a weighted F1 (mean $\pm$ SD) of up to 71.5 $\pm$ 3.7 for a single artery and 59.8 $\pm$ 1.7 for the joint artery classification. Performance was largely preserved when using automated instead of manual IAC segmentation masks, and we found the difference in weighted F1 not significant. Our results show that fully automated IAC subtype quantification from head CT is feasible and remains robust to the use of manual and automated IAC segmentation masks. Code at https://github.com/bjin96/iac-subtyping.

eess.IV↗