Non-stationary blind deconvolution of medical ultrasound scans

In linear approximation, the formation of a radio-frequency (RF) ultrasound image can be described based on a standard convolution model in which the image is obtained as a result of convolution of the point spread function (PSF) of the ultrasound scanner in use with a tissue reflectivity function (TRF). Due to the band-limited nature of the PSF, the RF images can only be acquired at a finite spatial resolution, which is often insufficient for proper representation of the diagnostic information contained in the TRF. One particular way to alleviate this problem is by means of image deconvolution, which is usually performed in a “blind” mode, when both PSF and TRF are estimated at the same time. Despite its proven effectiveness, blind deconvolution (BD) still suffers from a number of drawbacks, chief among which stems from its dependence on a stationary convolution model, which is incapable of accounting for the spatial variability of the PSF. As a result, virtually all existing BD algorithms are applied to localized segments of RF images. In this work, we introduce a novel method for non-stationary BD, which is capable of recovering the TRF concurrently with the spatially variable PSF. Particularly, our approach is based on semigroup theory which allows one to describe the effect of such a PSF in terms of the action of a properly defined linear semigroup. The approach leads to a tractable optimization problem, which can be solved using standard numerical methods. The effectiveness of the proposed solution is supported by experiments with in vivo ultrasound data.