WAVELET RESTORATION OF THREE-DIMENSIONAL MEDICAL PULSE-ECHO ULTRASOUND DATASETS IN AN EM FRAMEWORK

The application of pulse-echo ultrasound to the non-invasive imaging of soft biological tissues is now well established in modern clinical practice. In spite of this, however, the quality of pulse-echo ultrasound images remains poor because of inherent blurring and low image resolution, and there exists significant scope for the development of restoration algorithms to address this problem. Like other similar inverse problems, the performance of a particular restoration algorithm is highly contingent on the appropriateness of its underlying image model. The modelling of piecewise smooth natural images has been well studied in mainstream image processing, and it is known that the sparsifying properties of the wavelet transform are especially useful to provide simple but effective image models, leading to computationally efficient wavelet shrinkage methods for denoising. In a previous publication, we showed how wavelet-based models of natural images could be used in the context of pulse-echo ultrasound for image restoration; in particular, we proposed a simple model for the acoustic reflectivity functions of typical soft biological tissues that was able to account for their different behaviours on macroscopic and microscopic scales. We demonstrated how this model could be used in an expectation-maximisation (EM) restoration algorithm that simply alternated between Wiener filtering and wavelet shrinkage. Our previous results for two-dimensional images showed excellent performance compared to other methods based on less sophisticated image models, and in this paper, we extend our algorithm to the restoration of three-dimensional datasets to correct also for out-of-plane blurring.