Robust Kernel methods for sparse MR image reconstruction

A major challenge in contemporary magnetic resonance imaging (MRI) lies in providing the highest resolution exam possible in the shortest acquisition period. Recently, several authors have proposed the use of L₁-norm minimization for the reconstruction of sparse MR images from highly-undersampled k-space data. Despite promising results demonstrating the ability to accurately reconstruct images sampled at rates significantly below the Nyquist criterion, the extensive computational complexity associated with the existing framework limits its clinical practicality. In this work, we propose an alternative recovery framework based on homotopic approximation of the L₀-norm and extend the reconstruction problem to a multiscale formulation. In addition to several interesting theoretical properties, practical implementation of this technique effectively resorts to a simple iterative alternation between bilteral filtering and projection of the measured k-space sample set that can be computed in a matter of seconds on a standard PC.