Tissue harmonic image analysis based on spatial covariance

The van Cittert-Zernike theorem has been widely used to describe spatial covariance of the pressure field backscattered from a speckle object. Spatial covariance contains important information in the context of correlation-based correction of sound velocity inhomogeneities. Previous work was primarily based on spatial covariance analysis for linear imaging. In this paper, we extend the analysis to tissue harmonic imaging. Specifically, we investigate effects of the signal-to-noise ratio (SNR) and sound velocity inhomogeneities on spatial covariance. Results from tissue harmonic imaging are also compared with those from linear imaging. Both simulations and experiments are performed. At high SNRs, although both linear imaging and tissue harmonic imaging have spatial covariance functions close to theory, the spatial covariance of tissue harmonic imaging is consistently lower than that of linear imaging regardless of the presence of sound velocity inhomogeneities. At low SNRs, on the other hand, spatial covariance of tissue harmonic imaging is significantly affected. Because the tissue harmonic signal is much weaker than the linear counterpart, the low SNR reduces the accuracy of correlation-based estimation. It is concluded that the linear signal is more suitable for correlation-based correction of sound velocity inhomogeneities, despite the fact that tissue harmonic imaging generally has improved image quality over linear imaging.