Sparsity-based approaches have been popular in many applications in imageprocessing and imaging. Compressed sensing exploits the sparsity of images in atransform domain or dictionary to improve image recovery from undersampledmeasurements. In the context of inverse problems in dynamic imaging, recentresearch has demonstrated the promise of sparsity and low-rank techniques. Forexample, the patches of the underlying data are modeled as sparse in anadaptive dictionary domain, and the resulting image and dictionary estimationfrom undersampled measurements is called dictionary-blind compressed sensing,or the dynamic image sequence is modeled as a sum of low-rank and sparse (insome transform domain) components (L+S model) that are estimated from limitedmeasurements. In this work, we investigate a data-adaptive extension of the L+Smodel, dubbed LASSI, where the temporal image sequence is decomposed into alow-rank component and a component whose spatiotemporal (3D) patches are sparsein some adaptive dictionary domain. We investigate various formulations andefficient methods for jointly estimating the underlying dynamic signalcomponents and the spatiotemporal dictionary from limited measurements. We alsoobtain efficient sparsity penalized dictionary-blind compressed sensing methodsas special cases of our LASSI approaches. Our numerical experiments demonstratethe promising performance of LASSI schemes for dynamic magnetic resonance imagereconstruction from limited k-t space data compared to recent methods such ask-t SLR and L+S, and compared to the proposed dictionary-blind compressedsensing method.
展开▼
