BMND: Direct Poisson Denoising by N-Dimensional Block Matching and Collaborative Filtering

2026-09-28

AI Summary

This study addresses the challenge of denoising scientific data corrupted by signal-dependent Poisson noise across varying dimensionalities. We propose an arbitrary-dimensional block-matching and collaborative filtering framework that operates directly on raw Poisson data without requiring variance-stabilizing transformations. The method integrates dimension-agnostic reference traversal, aggregation-aware mass conservation, noise-aware patch matching, covariance propagation, and weighted overlap-add techniques to precisely preserve quantitative intensity information. As a unified, learning-free approach, it significantly improves reconstruction quality across 1D to 3D data while effectively mitigating intensity loss in low-count regimes. Code is publicly available.

Abstract

Poisson denoising of scientific data requires methods that account for signal-dependent noise while accommodating different data dimensionalities and preserving quantitative intensity information. We present BMND, a dimension-independent extension of block matching and collaborative filtering for Gaussian and Poisson observations. Building on the two-stage structure of BM3D and BM4D, BMND processes Poisson data directly, without a variance-stabilizing transform, by combining noise-aware patch matching with propagation of signal-dependent noise variances through collaborative filtering and aggregation. A dimension-independent reference-patch traversal scheme supports arrays with an arbitrary number of axes. An optional aggregation-aware mass conservation preserves the observed total intensity after weighted overlap-add. We evaluate the framework on one-dimensional physiological signals, two-dimensional images, and three-dimensional volumes, using controlled noise experiments and measured fluorescence microscopy acquisitions. The experiments demonstrate improved reconstruction quality from noise-aware matching and Wiener filtering, while low-count phantom experiments show reduced denoising-induced intensity loss through mass conservation. The framework provides a unified, non-learning-based approach to denoising across arbitrary data dimensions and is released as an open-source library.

Problem

• Poisson denoising
• signal-dependent noise
• N-dimensional data
• intensity preservation
• scientific data

Innovation

• Poisson denoising
• block matching
• collaborative filtering
• dimension-independent
• mass conservation