Performance of an adaptive multitaper method for reducing coherent noise in spectral analysis of ultrasound backscattered echoes

Abstract

This work is a simulation-based investigation of the performance of adaptive multitaper (aMTM) windows for reducing apparent coherence in spectral analysis of ultrasound echo signals. The multitaper method may be useful when echo signal segments are limited in their axial or lateral extent. The motivation is to create high spatial resolution, low-noise parametric images of Quantitative Ultrasound (QUS) parameters derived for incoherent scattering. Pulse-echo simulations convoluted a broadband (25%100% fractional bandwidth) acoustic pulse with a one-dimensional assortment of randomly distributed scatterers. Sets of 3000 independent, simulated echo signals were computed for different bandwidths and for various concentrations of scatterers (2-20 scatteres per pulse length). The power spectral density (PSD) was estimated as the average of individual periodograms from gated segments of a subset of the independent signals. PSD estimates were computed with the Short Time Fourier Transform using low-leakage tapering functions, Welch's method with different subsegment length and shift ratios, and Thomson's multitaper method. An adaptive time bandwidth selection criterion was designed to estimate PSD-derived parameters such as the backscatter coefficient using the multitaper method. The mean squared error (MSE) of PSD estimates was computed when reducing the window size from 1 to 50 pulse lengths axially and 1 to 50 averaged realizations laterally. For a particular MSE value, the window size leading to equal contributions of the bias and coherent noise was determined, and the diagonal of this window (Dw) was used as a criterion for comparison among PSD estimation methods. The adaptive multitaper method led to 77% and 13% reductions in Dw compared to that of the Short Time Fourier Transform (regardless of the windowing function) and Welch's method, respectively. These values did not vary significantly with different pulse bandwidths or scatterer densities above 10 scatterers per pulse lengths. The adaptive multitaper method successfully reduced bias and coherent noise compared to values for other methods, showing its advantage for spectral analysis of incoherent backscattered signals.