Task-Oriented Comparison of Power Spectral Density Estimation Methods for Quantifying Acoustic Attenuation in Diagnostic Ultrasound Using a Reference Phantom Method

Abstract

Reported here is a phantom-based comparison of methods for determining the power spectral density 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)=α0fβ, was estimated using a reference phantom method. The power spectral density as 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. For parameter estimation regions larger than ~34 pulse lengths (~1cm for this experiment), an overall power-law fit error 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 to those using the other techniques. Results provide guidance for choosing methods for estimating the power spectral density in quantitative ultrasound.

Scatterer Number Density Considerations in Reference Phantom-Based Attenuation Estimation

“…The power spectrum at a particular time point t 0 is given by an average over K tapers and M A-lines for a 2-D ROI. Improvements to attenuation estimation with the use of the MT method when compared to other gating windows have been discussed by Rosado-Mendez et al (2013). When computing a power spectrum with a Multi-taper estimator, improvement in estimation variance over just a single taper is expected when the spatial extent of the parameter estimation region is constrained (Rosado-Mendez et al, 2013).…”

“…Improvements to attenuation estimation with the use of the MT method when compared to other gating windows have been discussed by Rosado-Mendez et al (2013). When computing a power spectrum with a Multi-taper estimator, improvement in estimation variance over just a single taper is expected when the spatial extent of the parameter estimation region is constrained (Rosado-Mendez et al, 2013). All array and FFT operations were carried out using the Python library Numpy (Oliphant, 2007).…”

Quantitative ultrasound backscatter parameters in the human cervix

“…A recent paper suggests using the axial and lateral correlation lengths to determine window sizes based upon the chosen PS estimation method. [11] For echo signals from cervix tissue in this study, an axial correlation length of approximately 200 μm and a lateral scan line separation of 3 scan lines provided uncorrelated data. With these correlation lengths, relying upon the use of the multitaper PSD estimation method, a PS estimation region of 4x4 mm and a parameter estimation region of 8 mm (length) were deemed sufficient for subsequent analysis.…”

A multitaper Generalized Spectrum technique for detection of periodic structures in tissue: Comparison with conventional methods

“…Using correlation measurements of intensity (squared envelope) data as described by Rosado-Mendez et al [3], the corresponding pulse length was estimated at 0.25mm and the beam width at 0.74mm, spanning 6 adjacent acoustic lines B. Generalized Spectrum Analysis Two general approaches for the detection of coherent scattering from the periodically arranged fibers in the phantom were investigated: the Generalized Spectrum and the Singular Spectrum Analysis. The Generalized Spectrum (GS) S(f i ,f j ) is the expected value of the correlation of the Fourier transform Y(f) of a segment of RF signal y(t) at frequencies f i and f j :…”

“…To create parametric images based on periodicity features of the GS, a parameter estimation region is moved across a plane of RF echo data and one parameter estimate is obtained at each location of the region [3]. Ideally, the parameter estimation region, which includes segments of adjacent RF echo signals, should be small to provide good spatial resolution.…”