Analytic Global Regularized Backscatter Quantitative Ultrasound

Although a variety of techniques have been developed to reduce the appearance of B-mode speckle, quantitative ultrasound (QUS) aims at extracting hidden properties of the tissue. Herein, we propose two novel techniques to accurately and precisely estimate two important QUS parameters, namely the average attenuation coefficient and the backscatter coefficient. Both techniques optimize a cost function that incorporates data and continuity constraint terms, which we call AnaLytical Global rEgularized BackscatteR quAntitative ultrasound (ALGEBRA). We propose two versions of ALGEBRA, namely 1D- and 2D-ALGEBRA. In 1D-ALGEBRA, the regularized cost function is formulated in the axial direction, and QUS parameters are calculated for one line of radiofrequency (RF) echo data. In 2D-ALGEBRA, the regularized cost function is formulated for the entire image, and QUS parameters throughout the image are estimated simultaneously. This simultaneous optimization allows 2D-ALGEBRA to "see" all the data before estimating QUS parameters. In both methods, we efficiently optimize the cost functions by casting it as a sparse linear system of equations. As a result of this efficient optimization, 1D-ALGEBRA and 2D-ALGEBRA are respectively 600 and 300 times faster than optimization using the dynamic programing method previously proposed by our group. In addition, the proposed technique has fewer input parameters that require manual tuning. Our results demonstrate that the proposed ALGEBRA methods substantially outperform least-squares and dynamic programming methods in estimating QUS parameters in phantom experiments.