Compressed Sensing Dynamic MRI Reconstruction Using GPU-accelerated 3D Convolutional Sparse Coding

In this paper, we introduce a fast alternating method for reconstructing highly undersampled dynamic MRI data using 3D convolutional sparse coding. The proposed solution leverages Fourier Convolution Theorem to accelerate the process of learning a set of 3D filters and iteratively refine the MRI reconstruction based on the sparse codes found subsequently. In contrast to conventional CS methods which exploit the sparsity by applying universal transforms such as wavelet and total variation, our approach extracts and adapts the temporal information directly from the MRI data using compact shift-invariant 3D filters. We provide a highly parallel algorithm with GPU support for efficient computation, and therefore, the reconstruction outperforms CPU implementation of the state-of-the art dictionary learning-based approaches by up to two orders of magnitude.