Efficient compressed sensing SENSE parallel MRI reconstruction with joint sparsity promotion and mutual incoherence enhancement

Magnetic resonance imaging (MRI) is considered a key modality for the future as it offers several advantages, including the use of non-ionizing radiation and having no known side effects on the human body, and has recently begun to serve as a key component of multi-modal neuroimaging. However, two major intrinsic problems exist: slow acquisition and intrusive acoustic noise. Parallel MRI (pMRI) techniques accelerate acquisition by reducing the duration and coverage of conventional gradient encoding. The under-sampled k-space data is detected with several receiver coils surrounding the object, using distinct spatial encoding information for each coil element to reconstruct the image. However, this scanning remains slow compared to typical clinical imaging (e.g. X-ray CT). Compressed Sensing (CS), a sampling theory based on random sub-sampling, has potential to further reduce the sampling used in pMRI, accelerating acquisition further. In this work, we propose a new CS SENSE pMRI reconstruction model promoting joint sparsity across channels and enhancing mutual incoherence to improve reconstruction accuracy from limited k-space data. For fast image reconstruction and fair comparisons, all reconstructions are computed with split-Bregman and variable splitting techniques. Numerical results show that, with the introduced methods, reconstruction performance can be crucially improved with limited amount of k-space data.