Novel Algorithm for l1 Wavelet-Based MR Image Reconstruction

Introduction In fast MR imaging, reconstruction artifacts due to undersampled k-space can be greatly reduced by applying proper nonlinear reconstructions [1] based on image-sparsifying transforms. While state-of-the-art methods rely on total variation (TV), in this paper we propose to use wavelets instead, along with a very fast algorithm. Simulations and experimental results show our ability to reduce computational costs while maintaining SNR and image quality. We propose an iterative algorithm that also makes the technique computationally competitive. Our algorithm is versatile and can be used for any linear MR imaging problem, for instance SENSE [2]. Theory Our algorithm is based on the recent Iterative Shrinkage/Thresholding Algorithm (ISTA) [3] and Fast ISTA (FISTA) [4] that consists of repeating the sequence: gradient descent and wavelet domain thresholding. FISTA represents the current state-of-the-art for solving the variational problem ̃ x = argminx m−Ex 2 2 +λ Wx 1 1