Spatially Variant Ultrasound Image Restoration with Product Convolution
Résumé
The process of ultrasound 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 modelled as product-convolution. We argue that the ultrasound PSF varies smoothly enough for product-convolution to serve as an efficient and effective direct model for ultrasound 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.
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