Application of Tikhonov regularization to the restoration of phase contrast images

Abstract

New X-ray phase contrast imaging techniques without using synchrotron radiation confront a common problem from the negative effects of finite source sizes and limited spatial resolution. These negative effects swamp the fine phase contrast fringes and make them almost undetectable. In order to alleviate this problem, deconvolution procedures should be applied to the x-ray phase contrast images. In this study, four different deconvolution techniques were applied to experimental phase contrast images of a simple geometric phantom, including Weiner deconvolution method and Tikhonov regularization techniques with their Tikhonov matrix separately set as identity matrix, first order difference operator and second order difference operator. According to the free space propagation x-ray phase contrast imaging system, the source-to-sample distance (SS) of 200cm or 180cm was used with corresponding sample-to-detector distance (SD) of 20cm or 40cm. Image contrasts of 9.8%, 52.7%, 27.6% and 31.5% were separately obtained corresponding to above mentioned four techniques with SS/SD=200cm/20cm. For the second system setting (SS/SD=180cm/40cm), image contrasts of 11.9%, 112.8%, 66.3% and 76.5% were obtained separately. The Tikhonov regularization technique with Tikhonov matrix chosen as identity matrix obtains the highest contrast among all techniques. However, under this case, most noticeable artifacts and noise were introduced simultaneously. With full consideration on noise and artifacts, the Tikhonov matrix of second order difference operator will be the best choice for Tikhonov regularization method.