Task-Oriented Comparison of Power Spectral Density Estimation Methods for Quantifying Acoustic Attenuation in Diagnostic Ultrasound Using a Reference Phantom Method
1University of Wisconsin, Madison, WI, USA.Ultrasonic Imaging (Impact Factor: 0.91). 07/2013; 35(3):214-34. DOI: 10.1177/0161734613495524
Reported here is a phantom-based comparison of methods for determining the power spectral density (PSD) of ultrasound backscattered signals. Those power spectral density values are then used to estimate parameters describing α(f), the frequency dependence of the acoustic attenuation coefficient. Phantoms were scanned with a clinical system equipped with a research interface to obtain radiofrequency echo data. Attenuation, modeled as a power law α(f)= α0 f (β), was estimated using a reference phantom method. The power spectral density was estimated using the short-time Fourier transform (STFT), Welch's periodogram, and Thomson's multitaper technique, and performance was analyzed when limiting the size of the parameter-estimation region. Errors were quantified by the bias and standard deviation of the α0 and β estimates, and by the overall power-law fit error (FE). For parameter estimation regions larger than ~34 pulse lengths (~1 cm for this experiment), an overall power-law FE of 4% was achieved with all spectral estimation methods. With smaller parameter estimation regions as in parametric image formation, the bias and standard deviation of the α0 and β estimates depended on the size of the parameter estimation region. Here, the multitaper method reduced the standard deviation of the α0 and β estimates compared with those using the other techniques. The results provide guidance for choosing methods for estimating the power spectral density in quantitative ultrasound methods.
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ABSTRACT: Quantifying features related to acoustic scatterer periodicity can provide useful information to monitor tissue structural changes, but their detection is hindered by apparent coherence from random scatterers. This work compares the use a multitaper Generalized Spectrum (mtGS) to single-taper and time-average approaches (stGS and taGS, respectively) and to the Singular Spectrum Analysis (SSA) for detecting periodicity in backscattered echo signals when reducing the size of the parameter estimation region. A phantom with diffuse scatterers and an array of 0.1mm-diameter nylon fibers 0.4mm apart was scanned with a Siemens S2000 system using a linear array transducer. Radiofrequency (RF) echo signals from the fiber plane were obtained and Generalized Spectrum (GS) estimates were made either by stGS, taGS or mtGS with Discrete Prolate Spheroidal Sequences. Spectral components corresponding to periodic structures were identified by peaks in the GS Collapsed Average. SSA was implemented by obtaining eigenvalues and eigenvectors of the autocovariance matrix of signal segments. The periodic components of envelope signals were reconstructed using pairs of eigenvectors with similar eigenvalues. The frequency of the periodic component was estimated from the maximum value of its power spectrum. Histograms of frequency components detected by each method were constructed. The conspicuity of the 1.9MHz peak (corresponding to the fiber spacing) was measured as the size of the parameter estimation region was reduced axially and laterally from 20 to 2 correlation lengths. The mtGS improves detection of the relevant frequency components (1.9MHz and its harmonic) compared to stGS, taGSm and SSA by increasing their conspicuity over spurious components. This method also provided the minimum parameter estimation region size (8 pulse lengths axially, 6 uncorrelated scanlines laterally) viable for detection of periodic features.2013 IEEE International Ultrasonics Symposium (IUS); 07/2013
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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 scattere- s 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.2013 IEEE International Ultrasonics Symposium (IUS); 07/2013
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ABSTRACT: Attenuation estimation and imaging have the potential to be a valuable tool for tissue characterization, particularly for indicating the extent of thermal ablation therapy in the liver. Often the performance of attenuation estimation algorithms is characterized with numerical simulations or tissue-mimicking phantoms containing a high scatterer number density (SND). This ensures an ultrasound signal with a Rayleigh distributed envelope and a signal-to-noise ratio (SNR) approaching 1.91. However, biological tissue often fails to exhibit Rayleigh scattering statistics. For example, across 1647 regions of interest in five ex vivo bovine livers, we obtained an envelope SNR of 1.10 ± 0.12 when the tissue was imaged with the VFX 9L4 linear array transducer at a center frequency of 6.0 MHz on a Siemens S2000 scanner. In this article, we examine attenuation estimation in numerical phantoms, tissue-mimicking phantoms with variable SNDs and ex vivo bovine liver before and after thermal coagulation. We find that reference phantom-based attenuation estimation is robust to small deviations from Rayleigh statistics. However, in tissue with low SNDs, large deviations in envelope SNR from 1.91 lead to subsequently large increases in attenuation estimation variance. At the same time, low SND is not found to be a significant source of bias in the attenuation estimate. For example, we find that the standard deviation of attenuation slope estimates increases from 0.07 to 0.25 dB/cm-MHz as the envelope SNR decreases from 1.78 to 1.01 when estimating attenuation slope in tissue-mimicking phantoms with a large estimation kernel size (16 mm axially × 15 mm laterally). Meanwhile, the bias in the attenuation slope estimates is found to be negligible (<0.01 dB/cm-MHz). We also compare results obtained with reference phantom-based attenuation estimates in ex vivo bovine liver and thermally coagulated bovine liver.Ultrasound in medicine & biology 04/2014; 40(7). DOI:10.1016/j.ultrasmedbio.2014.01.022 · 2.21 Impact Factor
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