We present a novel reconstruction method for dynamic MR images from highly under-sampled k-space measurements. The reconstruction problem is posed as spectrally regularized matrix recovery problem, where kernel-based low rank constraint is employed to effectively utilize the non-linear correlations between the images in the dynamic sequence. Unlike other kernel-based methods, we use a single-step regularized reconstruction approach to simultaneously learn the kernel basis functions and the weights. The objective function is optimized using variable splitting and alternating direction method of multipliers. The framework can seamlessly handle additional sparsity constraints such as spatio-temporal total variation. The algorithm performance is evaluated on a numerical phantom and in vivo data sets and it shows significant improvement over the comparison methods.
Keywords: Dynamic MRI reconstruction; Kernel methods; Low rank decomposition.