Point spread functions and deconvolution of ultrasonic images


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

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