Frequency-domain algorithms for ultrasonic imaging based on interpolation-free stolt migration

Abstract

A class of algorithms for the post-processing of ultrasonic data in the frequency-domain are based on Stolt’s migration, which requires sampling the spectral data at non-uniformly spaced frequency points. Usually, the resampling of the frequency-domain data is obtained by using an oversampled Fast Fourier Transform and piecewise linear interpolation of the resulting frequency spectrum. This study proposes the use of frequency shifts to replace the interpolation step required by Stolt’s migration. An algorithm from synthetic aperture radar using the frequency shifting method is adapted and extended to ultrasonic imaging with frequency-domain algorithms. The proposed method is evaluated with experimental data, and it is demonstrated that migration by frequency shifts can present advantages over piecewise linear interpolation. In terms of reconstruction quality, algorithms using frequency shifts can achieve contrast-tonoise ratio similar to or superior than algorithms using piecewise linear interpolation. The computational load of algorithms using frequency shifts and piecewise linear interpolation is evaluated and algorithms using frequency shifts show at least a 1.5 times reduction in execution time, when the height of the imaging region under 30 mm. In addition, compared to piecewise linear interpolation, algorithms using frequency shifts presents advantages in CNR and execution time when the reconstructed image contains the bottom of the object.