Multifrequency Joint Reconstruction of Ultrasonic Attenuation Images

The estimation of attenuation coefficient slope (ACS) using the Spectral Log Difference (SLD) technique has presented high variability, leading to the use of regularization approaches. To address this issue, a previous study proposed the isolated denoising of the spectral log ratios at each frequency (TVSLD). In this study, we present a multifrequency joint method (WTNV-SLD) that leverages spatial structures from different frequencies during denoising, using a weighted total nuclear variation (WTNV) to improve the quality of ACS images. The selection of WTNV prior assumes that the spectral ratios across all frequencies are expected to exhibit the same geometrical shape. We compared the performance of the TVSLD and WTNV-SLD methods using mean percentage error (MPE) and Contrast-to-Noise Ratio (CNR) with simulated and physical phantom data. In the simulation, the results showed that WTNV-SLD outperformed TVSLD, achieving higher CNR (5.5 vs. 3.2) and lower MPE in both background (0.46% vs 1.8%) and inclusion (0.25% vs 7.1%) regions. In the physical phantom, WTNV-SLD and TVSLD obtained a similar MPE in the inclusion (0.10% and 0.41%, respectively) and in the background (6.5% and 7.9%, respectively), but achieved a higher CNR (4.1 vs. 2.6). Results suggest exploiting geometrical similarities among frequency channels improves ACS imaging, providing a better trade-off between MPE and CNR.