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Accelerating Low-Frequency Convergence for Limited-Angle DBT via Two-Channel Fidelity in PDHG

Taro Iyadomi, Ricardo Parada, Anna Kim, Lily Jiang, Emil Sidky, William Chang

Abstract

Reconstruction in limited-angle digital breast tomosynthesis (DBT) suffers from slow convergence of low spatial-frequency components when using weighted data-fidelity terms within primal-dual optimization. We introduce a two-channel fidelity strategy that decomposes the sinogram residual into complementary low-pass and high-pass bands using square-root Hanning (Hann^{1/2}) filter families, each driven by an independent \ell_2-ball constraint and dual update in the PDHG (Chambolle-Pock) algorithm with He-Yuan predictor-corrector relaxation. By assigning a larger dual step size and slightly looser tolerance to the low-frequency channel, the method delivers stronger per-iteration correction to the near-DC band without violating global PDHG stability. Experiments on a 2D digital breast phantom across multiple resolutions demonstrate that the two-channel approach yields 19%--61% RMSE improvement over the single-channel baseline, with larger gains at coarser discretizations where problem conditioning is more favorable, supporting more balanced spectral convergence in clinically realistic limited-angle regimes.

Accelerating Low-Frequency Convergence for Limited-Angle DBT via Two-Channel Fidelity in PDHG

Abstract

Reconstruction in limited-angle digital breast tomosynthesis (DBT) suffers from slow convergence of low spatial-frequency components when using weighted data-fidelity terms within primal-dual optimization. We introduce a two-channel fidelity strategy that decomposes the sinogram residual into complementary low-pass and high-pass bands using square-root Hanning (Hann^{1/2}) filter families, each driven by an independent \ell_2-ball constraint and dual update in the PDHG (Chambolle-Pock) algorithm with He-Yuan predictor-corrector relaxation. By assigning a larger dual step size and slightly looser tolerance to the low-frequency channel, the method delivers stronger per-iteration correction to the near-DC band without violating global PDHG stability. Experiments on a 2D digital breast phantom across multiple resolutions demonstrate that the two-channel approach yields 19%--61% RMSE improvement over the single-channel baseline, with larger gains at coarser discretizations where problem conditioning is more favorable, supporting more balanced spectral convergence in clinically realistic limited-angle regimes.
Paper Structure (14 sections, 4 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 14 sections, 4 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Directional Finite Differences and Directional Total Variation
  4. Constrained Sparsity-regularized Reconstruction
  5. The Single Channel Approach
  6. Notation for PDHG
  7. Why low spatial frequencies converge slowly
  8. Two-channel fidelity for spectrally balanced PDHG
  9. Spectral rationale
  10. Experimental Methodology
  11. Digital Phantom
  12. Algorithm Configuration
  13. Results
  14. Conclusion

Figures (2)

  • Figure 1: Image RMSE convergence for $256 \times 256$ reconstruction. Left: linear iteration scale. Right: log-log scale. The two-channel method (blue) achieves lower error and reduced early-iteration oscillation compared to the single-channel baseline (red).
  • Figure 2: Reconstruction comparison for $256 \times 256$ images. Top row: single-channel (left) and two-channel (right) reconstructions. Bottom row: corresponding difference images (reconstruction minus ground truth), displayed with grayscale range $[-0.75, 0.75]$. The two-channel result shows reduced large-scale intensity artifacts.