Compressed sensing MRI with total variation and frame balanced regularization

This paper presents a new sparse regularization model for frame-based image reconstruction in compressed sensing magnetic resonance imaging (CS-MRI). The proposed regularization includes both total variation (TV) norm and frame balanced penalty, called as TV-balanced approach. In frame-based l 1 -regularized image reconstruction, there are three formulations: analysis-based, synthesis-based and balance-based approaches. Although they are equivalent in orthogonal transform, they are different in redundant frame. Especially the balance-based approach can balance sparsity and smoothness of the reconstructed image by employing a penalty on distance between the sparse representation vector and analyzed coefficient vector. On the other hand, MR images commonly possess some blocky structures, and total-variation is often used to preserve image edges. Therefore by combining TV and balanced models, the proposed TV-balanced regularization can improve the reconstructed image quality from undersampled Λ-space measurements, which is solved numerically via exploiting variable splitting and alternating direction method of multiplier (ADMM) techniques. Efficiency of the proposed method has been evaluated on synthetic phantom and real human and rat brain MR images.