Smooth robust principal component analysis based on multidimensional transform tensor for dynamic MRI

Abstract

Dynamic magnetic resonance imaging (DMRI) stands as a sophisticated medical imaging technique pivotal to clinical practice, but the protracted duration of its imaging poses a substantial constraint on its practical application. This paper introduces a smooth robust principal component analysis model based on multidimensional transform tensors for accelerating DMR imaging. Specifically, the proposed method breaks down data into low-rank and sparse parts for reconstruction, respectively. The low-rank part employs a multidimensional adaptive transformation framework to generate transform tensors with favorable low-rank properties along three dimensions of DMR data. As for the sparse part, precise reconstruction can be achieved with the sparsity of the data after sparse transformation. In addition, to enhance the preservation of image details, this paper introduces a novel weighted tensor total variation regularization, imposing varying degrees of constraints based on smoothness in different dimensions. Experimental results demonstrate that the proposed method realizes superior reconstruction effects in comparison to existing advanced methods.