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Simultaneously spatial and temporal higher-order total variations for noise suppression and motion reduction in DCE and IVIM

In many applications based on kinetic evaluation analysis and model fitting, quantitative mapping retrieved on data series from modalites such as MRI is completed on a voxel-by-voxel basis, where motion and low signal to noise ratio (SNR) would considerably degenerate the reliability of estimations. The coherence of image series in space and time can be used as prior knowledge to mitigate this occurrence. In this study, spatial and temporal higher-order total variations (HOTVs) are applied on a data series of MRI signal (e.g. dynamic contrast-enhanced (DCE) MRI and intravoxel incoherent motion (IVIM) MRI) to exploit the coherence of signal in space and time to minimize the variabilities caused by motion as well as improving quality of images with low SNR while retaining the physical details of original data properly. Simultaneously applying spatial and temporal HOTVs on images is non-trivial in implementation since it is a non-smooth optimization problem with multiple regularizers. Therefore, we use the proximal gradient method as well as a primal-dual split proximal mechanism to address the problem properly. In addition to increase the reliability of quantitative parametric map estimations, this preprocessing procedure can be included into many existing map estimation algorithms and pipelines effortlessly. We demonstrate our method on the parametric maps estimation for DCE MRI and IVIM MRI.