Aberration correction by polynomial approximation for synthetic aperture ultrasound imaging
Authors: Leonov Denis , Kulberg Nicholas , Yakovleva Tatyana 
Published: April 2024

Background

Previously, there has been some work in the field of optical imaging on phase compensation by employing Legendre polynomials as an expansion of the phase function, and this seems to be an appealing unstudied area in the field of ultrasound imaging.

Purpose

The paper is devoted to solving one of the problems of enhancing the authenticity of diagnostics data obtained in ultrasound visualization systems and presents a novel approach to aberration correction, which ensures a reliable eliminating of phase distortions. The novelty of the proposed approach consists in the use of the decomposition of the wave front by Legendre polynomials to approximate aberrations of the phase front of ultrasonic waves propagating through distorting layers.

Methods

The phase aberrations are corrected using a single sector probe that captures echoes in synthetic aperture mode. The proposed method approximates the changes in the wave front by means of the Legendre polynomials. The performance was investigated by placing a 13‐mm‐wide ultrasonic probe with 64 elements operating at 2 MHz on the surface of a commercial quality control phantom ATS Model 539 through a distorting layer. The following metrics were measured: peak value, root mean square (RMS), full width at half maximum (FWHM), contrast‐to‐noise ratio (CNR). During the experiments, three different aberrators were used interchangeably as distorting layers, two of which were made of photopolymer resin with RMS values of 39 and 97 ns and a speed of sound close to that of a human temporal bone tissue, and the third was an ex vivo human temporal bone with the RMS value of 44 ns. To test the correction, three regions inside the phantom were examined. Two‐sided nonparametric Wilcoxon rank‐sum test was used for assessing the statistical significance. The significance level for this study was set at α ≤ 0.05. To counteract the problem of multiple comparisons, the p‐values were adjusted by the Holm–Bonferroni correction method.

Results

The statistically significant results have demonstrated the possibility of increasing peak intensity value up to 3.08 times, reducing the RMS width and FWHM of the intensity angular distribution down to 60% and 82%, respectively, and increasing CNR up to 2.12 times by using the proposed phase distortion correction method, compared with the case without correction. The results show that the method can be used as an effective aberration correction technique for all tested regions inside the phantom and distorting layers. Its usage allowed correcting up to 97% of the aberrations caused by the ex vivo temporal bone model.

Conclusion

The results show that the usage of the proposed method for aberration correction can successfully increase the intensity and reduce the angular width of the ultrasound wave scattered by the point targets inside the phantoms. The method works with different distorting layers and is capable of correcting phase aberrations in multiple sections of the sonogram. The limitation of the proposed method consists in the fact that it requires the use of aperture synthesis and access to raw radiofrequency data, which restricts its application in common scanners.