Spatially Variant Ultrasound Image Restoration With Product Convolution

The process of ultrasound (US) image formation can generally be modeled, using a linear and shift invariance approximation, as a convolution. In practice, the point spread function (PSF) is shift-variant. Here, we consider the restoration problem using a shift-variant PSF, where it is modeled as a product convolution. We argue that the US PSF varies smoothly enough for product convolution to serve as an efficient and effective direct model for US image restoration. We present a strategy for constructing the product-convolution operator and derive an efficient optimization scheme. We finally validate our approach on both simulated and real data, demonstrating state-of-the-art results while achieving significantly faster processing times.