Transconvolution

The term transconvolution designates a numerical method used in medical imaging, in particular emission computed tomography. Transconvolution enables a subsequent manipulation of the Point spread function (PSF) in already recorded images. Properties of an image such as the spatial resolution or the appearance of small objects are determined by the PSF of the imaging system used for image acquisition. Different imaging systems with different PSFs therefore provide slightly different images of one and the same object. Starting from known PSFs of different tomographic systems, the transconvolution method allows an image recorded on a particular tomograph to be converted as if it had been acquired by another tomograph. The method can thus ensure the comparability of images that were originally recorded on different systems.

The term transconvolution designates a numerical method used in medical imaging, in particular emission computed tomography. Transconvolution enables a subsequent manipulation of the Point spread function (PSF) in already recorded images. Properties of an image such as the spatial resolution or the appearance of small objects are determined by the PSF of the imaging system used for image acquisition. Different imaging systems with different PSFs therefore provide slightly different images of one and the same object. Starting from known PSFs of different tomographic systems, the transconvolution method allows an image recorded on a particular tomograph to be converted as if it had been acquired by another tomograph. The method can thus ensure the comparability of images that were originally recorded on different systems. obj * psf_1 = img_1 obj * psf_2 = img_2 with " * " representing the convolution operator and img_1 and img_2 representing the two slightly different images of the same object obj as seen by the respective tomographs. The two equations yield the relationship img_1 * psf_1^{-1} * psf_2 = img_2 with psf_1^{-1} representing the inverse function of the according point spread function psf_1 . The inverse point spreading function psf_1^{-1} diverges and can not be determined or handled numerically. But, within certain boundary conditions, the complete term psf_1^{-1} * psf_2 is approximately computable by numerical methods. The transconvolution function tf is defined as tf = psf_1^{-1} * psf_2 which results in the formula img_1 * tf = img_2 With the PSFs of the respective tomographs known, it is thus possible to convert an image img_1 recorded by the first tomograph into an img_2 emulating an image as recorded by the second tomograph. Of course, the method is subject to certain limits, in particular the computed img_2 can not represent spatial frequencies not captured to at least some degree by psf_1 . Consequently, the spatial resolution of an image can not be increased arbitrarily.

Text derived from https://en.wikipedia.org/w/index.php?oldid=1227951317 under CC BY-SA 4.0; modifications have been made.