# Closed-Form Nonlocal Shrinkage for Multiplicative Image Denoising and SAR Despeckling

arXiv: https://arxiv.org/abs/2608.15028 · HTML: https://mlsanity.com/paper/2608.15028/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 15 Aug 2026.

## Builds on (most cited first, 12 of 12)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Blind2Unblind: Self-Supervised Image Denoising with Visible Blind Spots](https://mlsanity.com/paper/2203.06967/) (2022)
- [Speckle2Void: Deep Self-Supervised SAR Despeckling with Blind-Spot Convolutional Neural Networks](https://mlsanity.com/paper/2007.02075/) (2020)
- [Transformer-based SAR Image Despeckling](https://mlsanity.com/paper/2201.09355/) (2022)
- [Positive2Negative: Breaking the Information-Lossy Barrier in Self-Supervised Single Image Denoising](https://mlsanity.com/paper/2412.16460/) (2024)
- [On Exact and Robust Recovery for Plug-and-Play Compressed Sensing](https://mlsanity.com/paper/2207.13031/) (2022)
- [A Tunable Despeckling Neural Network Stabilized via Diffusion Equation](https://mlsanity.com/paper/2411.15921/) (2024)
- [PolMERLIN: Self-Supervised Polarimetric Complex SAR Image Despeckling with Masked Networks](https://mlsanity.com/paper/2401.07503/) (2024)
- [Just Project! Multi-Channel Despeckling, the Easy Way](https://mlsanity.com/paper/2408.11531/) (2024)

## Abstract (arXiv)

Multiplicative noise poses a challenge in coherent and signal-dependent imaging owing to its intensity-dependent variance and frequently non-Gaussian distribution. We propose a deterministic nonlocal estimator that combines a logarithmic Yeo--Johnson transformation, patch grouping, an adaptive singular basis, and sparse shrinkage. The orthonormal group dictionary makes the weighted Lasso separable and yields an exact coefficient-wise soft-threshold solution. This solution replaces the iterative inner solver and expresses patch reliability and atom importance through a single threshold field. Since the dictionary is estimated from the noisy group, we introduce a random-matrix correction governed by the group aspect ratio γ=p2/K. The correction links patch size, group size, and shrinkage strength. Experiments cover gamma-corrupted images from three standard benchmarks and real synthetic aperture radar (SAR) imagery from five sensors. The method gives the best result in 18 of 24 PSNR/SSIM comparisons with twelve published methods and the lowest mean ratio-image deviation across six real SAR configurations. These results support geometry-calibrated nonlocal modeling for structure-preserving image restoration, with SAR despeckling serving as a demanding application. Code is available hrefhttps://github.com/Teriri1999/Geometry-Calibrated-Closed-Form-Shrinkage-for-SAR-Despecklinghere.