Tracking Tensor Subspaces with Informative Random Sampling for Real-Time MR Imaging
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Magnetic resonance imaging (MRI) nowadays serves as an important modality for diagnostic and therapeutic guidance in clinics. However, the slow acquisition process, the dynamic deformation of organs, as well as the need for real-time reconstruction, pose major challenges toward obtaining artifact-free images. To cope with these challenges, the present paper advocates a novel subspace learning framework that permeates benefits from parallel factor (PARAFAC) decomposition of tensors (multiway data) to low-rank modeling of temporal sequence of images. Treating images as multiway data arrays, the novel method preserves spatial structures and unravels the latent correlations across various dimensions by means of the tensor subspace. Leveraging the spatio-temporal correlation of images, Tykhonov regularization is adopted as a rank surrogate for a least-squares optimization program. Alteranating majorization minimization is adopted to develop online algorithms that recursively procure the reconstruction upon arrival of a new undersampled k-space frame. The developed algorithms are provably convergent and highly parallelizable with lightweight FFT tasks per iteration. To further accelerate the acquisition process, randomized subsampling policies are devised that leverage intermediate estimates of the tensor subspace, offered by the online scheme, to randomly acquire informative k-space samples. In a nutshell, the novel approach enables tracking motion dynamics under low acquisition rates `on the fly.' GPU-based tests with real in vivo MRI datasets of cardiac cine images corroborate the merits of the novel approach relative to state-of-the-art alternatives.
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