Enhancing ultrasonic attenuation images through multi-frequency coupling with total nuclear variation

Quantitative ultrasound is a non-invasive image modality that numerically characterizes tissues for medical diagnosis using acoustical parameters, such as the attenuation coefficient slope. A previous study introduced the total variation spectral log difference (TVSLD) method, which denoises spectral log ratios on a single-channel basis without inter-channel coupling. Therefore, this work proposes a multi-frequency joint framework by coupling information across frequency channels exploiting structural similarities among the spectral ratios to increase the quality of the attenuation images. A modification based on the total nuclear variation (TNV) was considered. Metrics were compared to the TVSLD method with simulated and experimental phantoms and two samples of fibroadenoma in vivo breast tissue. The TNV demonstrated superior performance, yielding enhanced attenuation coefficient slope maps with fewer artifacts at boundaries and a stable error. In terms of the contrast-to-noise ratio enhancement, the TNV approach obtained an average percentage improvement of 34% in simulation, 38% in the experimental phantom, and 89% in two in vivo breast tissue samples compared to TVSLD, showing potential to enhance visual clarity and depiction of attenuation images.