Frequency‐splitting dynamic MRI reconstruction using multi‐scale 3D convolutional sparse coding and automatic parameter selection

HighlightsConvolutional dictionary reconstructs high‐frequency component of MRI images well.Temporal total variation reconstructs low‐frequency component of MRI images well.Multi‐scale dictionary improves MRI reconstruction quality.Elastic net regularization works better than L1 or L2 regularization only.Genetic algorithm automatically finds optimal parameters for MRI reconstruction. Graphical abstract Figure. No Caption available. ABSTRACT In this paper, we propose a novel image reconstruction algorithm using multi‐scale 3D convolutional sparse coding and a spectral decomposition technique for highly undersampled dynamic Magnetic Resonance Imaging (MRI) data. The proposed method recovers high‐frequency information using a shared 3D convolution‐based dictionary built progressively during the reconstruction process in an unsupervised manner, while low‐frequency information is recovered using a total variation‐based energy minimization method that leverages temporal coherence in dynamic MRI. Additionally, the proposed 3D dictionary is built across three different scales to more efficiently adapt to various feature sizes, and elastic net regularization is employed to promote a better approximation to the sparse input data. We also propose an automatic parameter selection technique based on a genetic algorithm to find optimal parameters for our numerical solver which is a variant of the alternating direction method of multipliers (ADMM). We demonstrate the performance of our method by comparing it with state‐of‐the‐art methods on 15 single‐coil cardiac, 7 single‐coil DCE, and a multi‐coil brain MRI datasets at different sampling rates (12.5%, 25% and 50%). The results show that our method significantly outperforms the other state‐of‐the‐art methods in reconstruction quality with a comparable running time and is resilient to noise.