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Learnable Total Variation with Lambda Mapping for Low-Dose CT Denoising

Yusuf Talha Basak, Mehmet Ozan Unal, Metin Ertas, Isa Yildirim

TL;DR

The paper tackles LDCT denoising by learning when and where to apply TV smoothing. It introduces Learnable Total Variation (LTV), which couples an unrolled primal--dual TV solver with a LambdaNet that predicts a per-pixel regularization map $\lambda$, enabling spatially adaptive denoising guided by both the physics-informed solver and learned priors. The end-to-end training uses a composite loss that combines image fidelity terms with priors on the $\lambda$-map to ensure spatial coherence, structure alignment, and distributional diversity of regularization. Empirically, LTV achieves substantial gains over classical TV and FBP+U-Net on LDCT data (e.g., up to $+2.9$ dB PSNR and $+6 ext{–}7 ext%$ SSIM improvement), while retaining interpretability and offering a principled path toward 3D and data-consistency–driven reconstruction.

Abstract

Although Total Variation (TV) performs well in noise reduction and edge preservation on images, its dependence on the lambda parameter limits its efficiency and makes it difficult to use effectively. In this study, we present a Learnable Total Variation (LTV) framework that couples an unrolled TV solver with a data-driven Lambda Mapping Network (LambdaNet) predicting a per-pixel regularization map. The pipeline is trained end-to-end so that reconstruction and regularization are optimized jointly, yielding spatially adaptive smoothing: strong in homogeneous regions, relaxed near anatomical boundaries. Experiments on the DeepLesion dataset, using a realistic noise model adapted from the LoDoPaB-CT methodology, show consistent gains over classical TV and FBP+U-Net: +2.9 dB PSNR and +6% SSIM on average. LTV provides an interpretable alternative to black-box CNNs and a basis for 3D and data-consistency-driven reconstruction.

Learnable Total Variation with Lambda Mapping for Low-Dose CT Denoising

TL;DR

The paper tackles LDCT denoising by learning when and where to apply TV smoothing. It introduces Learnable Total Variation (LTV), which couples an unrolled primal--dual TV solver with a LambdaNet that predicts a per-pixel regularization map , enabling spatially adaptive denoising guided by both the physics-informed solver and learned priors. The end-to-end training uses a composite loss that combines image fidelity terms with priors on the -map to ensure spatial coherence, structure alignment, and distributional diversity of regularization. Empirically, LTV achieves substantial gains over classical TV and FBP+U-Net on LDCT data (e.g., up to dB PSNR and SSIM improvement), while retaining interpretability and offering a principled path toward 3D and data-consistency–driven reconstruction.

Abstract

Although Total Variation (TV) performs well in noise reduction and edge preservation on images, its dependence on the lambda parameter limits its efficiency and makes it difficult to use effectively. In this study, we present a Learnable Total Variation (LTV) framework that couples an unrolled TV solver with a data-driven Lambda Mapping Network (LambdaNet) predicting a per-pixel regularization map. The pipeline is trained end-to-end so that reconstruction and regularization are optimized jointly, yielding spatially adaptive smoothing: strong in homogeneous regions, relaxed near anatomical boundaries. Experiments on the DeepLesion dataset, using a realistic noise model adapted from the LoDoPaB-CT methodology, show consistent gains over classical TV and FBP+U-Net: +2.9 dB PSNR and +6% SSIM on average. LTV provides an interpretable alternative to black-box CNNs and a basis for 3D and data-consistency-driven reconstruction.

Paper Structure

This paper contains 15 sections, 5 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Overview
  5. LambdaNet and Adaptive $\lambda$-Mapping
  6. Unrolled Primal--Dual TV Denoiser
  7. Comprehensive Training Objective
  8. Image Fidelity
  9. $\lambda$-Map Spatial Smoothness
  10. Structure-Lambda Alignment
  11. $\lambda$-Map Distributional Regularization
  12. Experiments and Results
  13. Quantitative and Qualitative Analysis
  14. Lambda Adaptivity and Ablation
  15. Conclusion

Figures (3)

  • Figure 1: Overview of the LTV framework. LambdaNet predicts a spatially adaptive $\lambda$-map that guides an unrolled TV solver for denoising, trained end-to-end with combined fidelity and regularization losses.
  • Figure 2: Representative LDCT slices comparing noisy, TV, U-Net, and LTV reconstructions.
  • Figure 3: Absolute error maps. LTV yields smaller and more uniform residuals, whereas FBP+U-Net shows high-error zones near edges and lesions.