On an analytical, spatially-varying, formulation of the point-spread-function with an application to deconvolution

The point spread function (PSF), namely the response of a system to a point source, is a measure of the quality of an ultrasound imager system. It highly depends on the image reconstruction algorithm, and it is usually either crudely estimated by assuming spatial-invariance, or evaluated via simulation, as proposed by Field II, coupled with reconstruction algorithms, such as delay-and-sum (DAS). The lack of an analytical formulation of the PSF inhibits many applications ranging from optimization of apodization schemes, to array-design and deconvolution algorithms