Determination of point spread function in computed tomography accompanied with verification

A method for verifying the point spread function (PSF) measured by computed tomography has been previously reported [Med. Phys. 33, 2757-2764 (2006)]; however, this additional PSF verification following measurement is laborious. In the present study, the previously described verification method was expanded to PSF determination. First, an image was obtained by scanning a phantom. The image was then two-dimensionally deconvolved with the object function corresponding to the phantom structure, thus allowing the PSF to be obtained. Deconvolution is implemented simply by division of spatial frequencies (corresponding to inverse filtering), in which two parameters are used as adjustable ones. Second, an image was simulated by convolving the object function with the obtained PSF, and the simulated image was compared to the above-measured image of the phantom. The difference indicates the inaccuracy of the PSF obtained by deconvolution. As a criterion for evaluating the difference, the authors define the mean normalized standard deviation (SD) in the difference between simulated and measured images. The above two parameters for deconvolution can be adjusted by referring to the subsequent mean normalized SD (i.e., the PSF is determined so that the mean normalized SD is decreased). In this article, the parameters were varied in a fixed range with a constant increment to find the optimal parameter setting that minimizes the mean normalized SD. Using this method, PSF measurements were performed for various types of image reconstruction kernels (21 types) in four kinds of scanners. For the 16 types of kernels, the mean normalized SDs were less than 2.5%, indicating the accuracy of the determined PSFs. For the other five kernels, the mean normalized SDs ranged from 3.7% to 4.8%. This was because of a large amount of noise in the measured images, and the obtained PSFs would essentially be accurate. The method effectively determines the PSF, with an accompanying verification, after one scanning of a phantom.