Attenuation Coefficient Imaging Using Regularization by Denoising

This study examines the effect of the regularization prior on attenuation coefficient slope (ACS) imaging based on spectral log difference (SLD) when the imaging region of interest (ROI) contains heterogeneous backscatter (BSC). In regularized SLD (RSLD), total variation (TV) regularization of the ACS map can propagate BSC-induced bias beyond the underlying echogenicity transition when the imaging ROI contains heterogeneous BSC. To address this limitation, we propose a regularization by denoising (RED) formulation that replaces the TV prior on the ACS map with a median-filter prior, while regularizing the BSC-related term with soft-thresholding. The inverse problem was solved with the RED phase-gradient algorithm and evaluated against RSLD in simulations, a layered phantom, and in vivo liver and thyroid data by comparing restricted imaging ROIs approximately homogeneous in BSC with extended imaging ROIs containing heterogeneous BSC. In the simulated heterogeneous imaging-ROI cases, RED reduced mean absolute percentage error (MAPE) from 51.5% to 14.9% in liver and from 42.7% to 5.4% in thyroid. In the layered phantom, RED reduced MAPE from 21.5% to 2.5% in the lower layer and from 41.0% to 13.0% in the upper layer. In in vivo data, ROI-dependent ACS variation decreased from 41.0% to 3.5% in liver and from 48.7% to 2.3% in thyroid. Complementary inclusion experiments also showed improved local confinement of boundary-related bias. These results indicate that RED is more robust than RSLD for SLD attenuation imaging under heterogeneous BSC while preserving competitive performance in homogeneous conditions.