Radial energy-quantile estimation for geometry-aware local wavenumber mapping in harmonic shear wave elastography.

Local wavenumber estimation in harmonic shear-wave elastography is strongly influenced by wavefield geometry. We introduce the radial energy-quantile (REQ) estimator, a local spectral method designed to estimate wavenumber across directional, intermediate, and projected diffuse wavefield regimes. Approach. REQ defines the local wavenumber as the radial spatial frequency at which the cumulative angularly averaged power spectrum reaches a prescribed quantile, denoted by q. The value of q is selected a priori from discrete-consistent theoretical models that account for finite windowing, Fourier sampling, and radial binning. The dependence of q on wavefield geometry was characterized using aperture-controlled simulations. REQ was subsequently evaluated using full-wave k-Wave simulations, tissue-mimicking gelatin phantoms with independent mechanical reference measurements, and ex vivo bovine liver and kidney experiments. REQ was benchmarked against the Angular Integral Autocorrelation (AIA) estimator in the k-Wave simulations and in the inclusion phantom. Main results The required quantile increased as the angular support of the wavefield broadened from predominantly directional propagation toward the projected diffuse 3D regime. In k-Wave simulations, REQ produced lower inclusion-region absolute percentage error than the angular integral autocorrelation estimator in all four evaluated wavefield classes, with maximum errors of 5.97% and 28.27%, respectively. The mean estimator runtime was 0.66 ± 0.10 s for REQ, compared with 72.34 ± 9.20 s for the comparator. In phantom experiments, REQ preserved the expected contrast between the soft and stiff regions under both excitation configurations. In the inclusion phantom, REQ also showed lower spatial variability, smaller distances to the mechanical reference bands, and better contrast recovery than AIA under both excitation configurations. In the ex vivo experiments, REQ recovered tissue-background differences and frequency-dependent responses in both liver and kidney. Significance. REQ provides a physically interpretable and computationally efficient framework for geometry-aware local wavenumber estimation across a broad range of harmonic wavefield conditions.&#xD.