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

arXiv: https://arxiv.org/abs/2609.34622 · HTML: https://mlsanity.com/paper/2609.34622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 51 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 1 of 1)

- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)

## Abstract (arXiv)

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.