A wavelet-based EM algorithm for the restoration of medical pulse-echo ultrasound datasets

The application of pulse-echo ultrasound to anatomical imaging is well established, but despite the prevalence of this imaging modality in modern clinical practice, typical ultrasound images still suffer from blurring and poor resolution and there is significant scope for developing restoration algorithms to address this problem. As with other similar inverse problems, the design of an effective restoration algorithm is contingent on a good image model, and in this respect, the problem is challenging because the acoustic reflectivities of soft tissues have statistical characteristics that are substantially different to those of natural images studied in mainstream image processing. Whereas natural images tend to be piecewise-smooth and are well sparsified by a wavelet basis, the acoustic reflectivities of soft tissues exhibit piecewise-smoothness only on a macroscopic scale; on a microscopic scale, they exhibit a pseudo-random texture. Previously, we presented a simple model of acoustic reflectivity which could adequately account for this dual behaviour and we described a statistically-motivated restoration algorithm that simply alternated between Wiener filtering and dual-tree complex wavelet shrinkage [1]. Our previous results for two-dimensional images showed improved performance compared to other methods based on less sophisticated image models, and in this paper, we extend our algorithm to three-dimensional datasets to correct also for out-of-plane (elevational) blurring.