Deconvolution of medical ultrasound images using ℓ1-norm optimization and envelope PSF estimation

Medical ultrasound imaging is a non-invasive technique for clinical diagnosis, but its applications are limited by the low image quality. In this paper, the problem of ultrasound imaging is dealt with by a novel deconvolution method which utilizes the envelope of the point spread function (EPSF) instead of the commonly used point spread function (PSF). The EPSF is estimated based on minimum phase assumption without considering phase unwrapping and linear phase elimination, thus it is much efficient and reliable. After obtaining the EPSF, an ℓ₁-norm regularized optimization model is derived and efficiently solved by an augmented Lagrangian method (ALM). Experiments are conducted on both simulated and in vivo data. The results show that the proposed deconvolution method can provide significantly improved ultrasound images in terms of resolution gain and signal to noise ratio.