Blind deconvolution of medical ultrasound images using variable splitting and proximal point methods

The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, a hybrid deconvolution method is employed to recover a reliable estimate of the tissue reflectivity function directly from ultrasound RF data. Here, the “hybridization” suggests a two-stage reconstruction scheme, in which some partial information about the point spread function (PSF) of the imaging system is recovered first, followed by its use to explicitly constrain the procedure of inverse filtering. The latter is realized in the form of an optimization problem, whose efficient and stable solution is addressed in this note. In particular, we proposed to solve the problem of inverse filtering using the alternating direction method of multipliers (ADMM). We show that this method leads to a particularly efficient numerical scheme, which is implemented as a succession of analytically computable proximity operations. Additionally, it is shown how the inverse filters designed in this way can be used to deconvolve the ultrasound images in a non-blind manner so as to further improve their resolution and contrast. The effectiveness of the proposed deconvolution procedures is exemplified by in vivo experiments.