Construction of adaptively regularized parametric maps for quantitative ultrasound imaging

In the field of quantitative ultrasound (QUS), constructing semantic parametric maps based on local attenuation coefficient slope (ACS) or backscatter coefficient (BSC) modeling remains a challenge. These maps may be useful for detecting lesions or anatomical objects, or for characterizing anomalies within organs. The objective was to propose a methodology for constructing regularized parametric maps in the case of linear fitting models. The proposed method was tested on: i) the spectral Gaussian fit (SGF) BSC model, comprising the acoustical concentration and effective scatterer size; and ii) the spectral log-difference (SLD) model, yielding the local ACS. Regularization was formulated as generalized LASSO, upon setting a locally constant trend constraint on regression coefficients, with variable Lagrangian multiplier (LM). The latter was set with a variant of the Bayesian Information Criterion (BIC): the LM was maximized as to yield a BIC no worse than that of the maximum likelihood. Phantoms were made with agar and graphite powder (g.p.). Acquisitions were performed with a Verasonics Vantage 256 (Redmond, WA) scanner using an ATL L7-4 probe (Philips, Bothell, WA) driven at 5 MHz. Using 21 angles (-5oto 5o) compounding, 100 frames were acquired. Beamformed radiofrequency data were averaged over all frames. Power spectra were averaged over 15 scan lines, each spanning 10 pulse lengths, on overlapping windows. Acquisitions with same settings were made on a reference phantom (117GU-101 CIRS, Norfolk, VA). Ground truth ACS values were estimated with a planar reflection method yielding (in dB/cm/MHz): #1) 0.56 ± 0.06 (4.5% g.p.); and #2) 1.27 ± 0.09 (12% g.p.). i) SGF results: On phantoms with an inclusion (N = 4, #2 surrounded by #1), the contrast-to-noise ratio on difference in acoustic concentration (log-scale) was 2.7 ± 0.22 (no units) with regularization, and 0.97 ± 0.13 without it. ii) SLD results: On phantoms with side-by-side media (N = 3), biases were: #1) -0.11 ± 0.04; #2) -0.26 ± 0.03; and standard-deviations (SD) were: #1) 0.05 ± 0.04; #2) 0.09 ± 0.02. Without regularization, biases were #1) -0.09 ± 0.17; #2) -0.25 ± 0.20; SD values were: #1) 0.39 ± 0.04; #2) 0.38 ± 0.08.

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