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.