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Deep Unfolded BM3D: Unrolling Non-local Collaborative Filtering into a Trainable Neural Network

Kerem Basim, Mehmet Ozan Unal, Metin Ertas, Isa Yildirim

TL;DR

This paper tackles denoising for low-dose CT (LDCT) by integrating a model-based non-local prior with a trainable denoiser through deep unfolding. The method, DU-BM3D, keeps BM3D's block-matching and aggregation fixed while replacing the collaborative filtering with a U-Net denoiser, trained end-to-end. Training targets the LDCT-to-normal-dose mapping across dose regimes using a single model trained at $100k$ photons and evaluated across $10k$–$500k$ photon counts; performance is measured by PSNR and SSIM. Results show DU-BM3D outperforms classic BM3D and standalone U-Net, with strongest gains in high-noise settings and robust cross-dose generalization, highlighting the practicality of hybrid priors for medical image restoration.

Abstract

Block-Matching and 3D Filtering (BM3D) exploits non-local self-similarity priors for denoising but relies on fixed parameters. Deep models such as U-Net are more flexible but often lack interpretability and fail to generalize across noise regimes. In this study, we propose Deep Unfolded BM3D (DU-BM3D), a hybrid framework that unrolls BM3D into a trainable architecture by replacing its fixed collaborative filtering with a learnable U-Net denoiser. This preserves BM3D's non-local structural prior while enabling end-to-end optimization. We evaluate DU-BM3D on low-dose CT (LDCT) denoising and show that it outperforms classic BM3D and standalone U-Net across simulated LDCT at different noise levels, yielding higher PSNR and SSIM, especially in high-noise conditions.

Deep Unfolded BM3D: Unrolling Non-local Collaborative Filtering into a Trainable Neural Network

TL;DR

This paper tackles denoising for low-dose CT (LDCT) by integrating a model-based non-local prior with a trainable denoiser through deep unfolding. The method, DU-BM3D, keeps BM3D's block-matching and aggregation fixed while replacing the collaborative filtering with a U-Net denoiser, trained end-to-end. Training targets the LDCT-to-normal-dose mapping across dose regimes using a single model trained at photons and evaluated across – photon counts; performance is measured by PSNR and SSIM. Results show DU-BM3D outperforms classic BM3D and standalone U-Net, with strongest gains in high-noise settings and robust cross-dose generalization, highlighting the practicality of hybrid priors for medical image restoration.

Abstract

Block-Matching and 3D Filtering (BM3D) exploits non-local self-similarity priors for denoising but relies on fixed parameters. Deep models such as U-Net are more flexible but often lack interpretability and fail to generalize across noise regimes. In this study, we propose Deep Unfolded BM3D (DU-BM3D), a hybrid framework that unrolls BM3D into a trainable architecture by replacing its fixed collaborative filtering with a learnable U-Net denoiser. This preserves BM3D's non-local structural prior while enabling end-to-end optimization. We evaluate DU-BM3D on low-dose CT (LDCT) denoising and show that it outperforms classic BM3D and standalone U-Net across simulated LDCT at different noise levels, yielding higher PSNR and SSIM, especially in high-noise conditions.

Paper Structure

This paper contains 6 sections, 5 equations, 3 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. METHODOLOGY
  4. EXPERIMENTS
  5. DISCUSSION
  6. CONCLUSION

Figures (3)

  • Figure 1: Training procedure for the U-Net denoiser component.
  • Figure 2: Denoising results at different photon levels. Top row: 10k photon level (extreme low-dose). Bottom row: 100k photon level (moderate low-dose). From left to right in each row: Noisy input, Ground Truth, BM3D, U-Net, and DU-BM3D (ours).
  • Figure 3: Comparison of models regarding (a) number of learnable parameters and (b) average inference time per test image.