Dear Igor,You and your readers might be interested in my paper recently published (early view) which is about the use of the RPCA (or L+S) model in dynamic MR imaging from partial Fourier samples for both reconstruction and separation:Dynamic MR image reconstruction–separation from undersampled (k,t)-space via low-rank plus sparse prior(This is an open access article thanks to the new policy in the UK)I have made available an implementation of the algorithm in matlab hereNote that interestingly Otazo et al. have published almost simultaneously a very similar work in a different journal:Otazo et al, Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components, 2014Yet there are some differences, so these papers are kind of complementary.Thanks!Best regards,Benjamin Trémoulhéac
Thank you Benjamin. Here is the paper:
Dynamic MR image reconstruction--separation from under-sampled (k-t)-space via low-rank plus sparse prior by Tremoulheac, B. ; B. Tr´emoulheac, Dikaios, N. ; Atkinson, D. ; Arridge, S.
Dynamic magnetic resonance imaging (MRI) is used in multiple clinical applications, but can still benefit from higher spatial or temporal resolution. A dynamic MR image reconstruction method from partial (k-t)-space measurements is introduced that recovers and inherently separates the information in the dynamic scene. The reconstruction model is based on a low-rank plus sparse decomposition prior, which is related to robust principal component analysis. An algorithm is proposed to solve the convex optimization problem based on an alternating direction method of multipliers. The method is validated with numerical phantom simulations and cardiac MRI data against state of the art dynamic MRI reconstruction methods. Results suggest that using the proposed approach as a means of regularizing the inverse problem remains competitive with state of the art reconstruction techniques. Additionally, the decomposition induced by the reconstruction is shown to help in the context of motion estimation in dynamic contrast enhanced MRI.