Improving local attenuation estimation using a spatial regularization strategy over frequencies

Spectral-based techniques for attenuation coefficient slope (ACS) imaging, such as spectral log difference (SLD), experience high estimation variance. A previous work introduced a novel regularized SLD (RSLD) method for the joint estimation of ACS values in all regions of interest (ROIs) within the field of view, in contrast with classic attenuation imaging methods which obtain ACS values from each ROI independently. Reported results showed a decrease in the spatial variance of ACS estimates at the expense of an increase in estimation bias. This study presents a modified regularized strategy designed to extend the tradeoff between ACS estimation accuracy and precision. In the SLD technique, ACS values are estimated through a linear regression versus frequency of the logarithm of the spectral ratio between proximal and distal windows within the ROI after proper diffraction compensation. In RSLD, the ACSs from all ROIs are jointly estimated using a generalized Tikhonov regularization with a penalty term equal to the L1-norm of the gradients in the axial and lateral directions. In this study, the ACS for each ROI was estimated independently, but the spectral ratio at each frequency bin within the analysis bandwidth was denoised prior to the estimation process using total variation (TVSLD). Both methods assume the ACS images conform to a piecewise homogeneous model. Two agar based cylindrical phantoms (P1 and P2) with an embedded inclusion were imaged to evaluate the proposed strategy. Background and inclusion ACSs were estimated using insertion loss techniques and found to be 0.41 and 0.75 dB/cm/MHz for P1, and 0.54 and 1.04 dB/cm/MHz for P2, respectively. Data was collected using a 7.5 MHz, f/4 single element transducer. The ACS images of both phantoms derived using the SLD, RSLD, and TVSLD techniques are shown in Fig. 1. The RSLD method allowed a significant reduction in the ACS standard deviation (>70%) at the expense of higher bias in the inclusion regions (>20%), and a threefold increase in CNR when compared to SLD. In contrast, the TVSLD allowed obtaining the same precision improvement with a smaller bias (less than 12%) in the inclusion and a fivefold increase in CNR. These results suggest that the use of regularization tools may have a significant benefit in the performance of attenuation coefficient imaging techniques.