On an analytical, spatially-varying, point-spread-function

The point spread function (PSF), namely the response of an ultrasound system to a point source, is a powerful measure of the quality of an imaging system. The lack of an analytical formulation inhibits many applications ranging from apodization optimization, array-design, and deconvolution algorithms. We propose to fill this gap through a general PSF derivation that is flexible with respect to the type of transmission (synthetic aperture, plane-wave, diverging-wave etc.), while faithfully capturing the spatially-variant blurring of the Tissue Reflectivity Function as caused by Delay-And-Sum reconstruction. We validate the derived PSF against simulation using Field II, and show that accounting for PSF spatial-variability in sparse-based deconvolution improves reconstruction.