Regularized phantom-free construction of local attenuation coefficient slope maps for quantitative ultrasound imaging

Constructing an attenuation map based on local attenuation coefficient slope (ACS) in quantitative ultrasound (QUS) has shown potential in the diagnosis of liver steatosis. Detecting tumors in the liver and differentiating abnormalities in tissues are some other applications for these maps. In this work, we considered the construction of semantic parametric maps and a recent method providing a phantom-free estimation of local ACS. The main goal was to propose a methodology for constructing regularized phantom-free local ACS maps based on this framework. The proposed method was tested on two tissue mimicking (#1 and #2) with different attenuation: i) homogeneous phantoms; and ii) side-by-side phantoms. Modifications brought to previous works include: a) a linear interpolation of the power spectrum in log-scale; b) the relaxation of the underlying hypothesis on the diffraction factor; c) a generalization to nonhomogeneous local ACS; and d) an adaptive restriction of frequencies to a more reliable range for this purpose than the usable frequency range. The regularization was formulated as generalized LASSO, and a variant of the Bayesian Information Criterion (BIC) was applied to estimate the Lagrangian multiplier on the LASSO constraint. Ultrasound acquisitions were performed with a Verasonics Vantage 256 scanner (Redmond, WA) using an ATL L7-4 probe (Philips, Bothell, WA) driven at 5 MHz, using 21 angles (-5° to 5°) compounding. In this work, power spectra were averaged over 25 scanlines, each spanning 10 pulse lengths. i) On homogeneous phantoms, normalized root mean squared errors (NRMSE) were (in %): #1) 8.9 ± 3.6; #2) 7.0 ± 1.6. Without regularization, the phantom-free method yielded NRMSEs of: #1) 19.1 ± 2.1; #2) 11.5 ± 1.0. ii) On phantoms with side-by-side media, NRMSEs were: #1) 32.3 ± 8.5; #2) 10.3 ± 6.8. Without regularization, NRMSEs were #1) 35.1 ± 8.7; #2) 13.2 ± 5.2. The contrast-to-noise-ratio was 4.4 ± 1.7 (no units) with regularization, and 2.6 ± 0.6 without it. Future work should address the problem of boundaries between distinct media (tissues).