Point spread functions and deconvolution of ultrasonic images

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Christoph DalitzThorsten Michalk

Abstract

This article investigates the restoration of ultrasonic pulse-echo C-scan images by means of deconvolution with a point spread function (PSF). The deconvolution concept from linear system theory (LST) is linked to the wave equation formulation of the imaging process, and an analytic formula for the PSF of planar transducers is derived. For this analytic expression, different numerical and analytic approximation schemes for evaluating the PSF are presented. By comparing simulated images with measured C-scan images, we demonstrate that the assumptions of LST in combination with our formula for the PSF are a good model for the pulse-echo imaging process. To reconstruct the object from a C-scan image, we compare different deconvolution schemes: the Wiener filter, the ForWaRD algorithm, and the Richardson-Lucy algorithm. The best results are obtained with the Richardson-Lucy algorithm with total variation regularization. For distances greater or equal twice the near field distance, our experiments show that the numerically computed PSF can be replaced with a simple closed analytic term based on a far field approximation.

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Citations

Jul 21, 2020·Microscopy and Microanalysis : the Official Journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada·Joshua StucknerMitsuhiro Murayama

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