Wavelet-regularized reconstruction for rapid MRI

We propose a reconstruction scheme adapted to MRI that takes advantage of a sparsity constraint in the wavelet domain. We show that artifacts are significantly reduced compared to conventional reconstruction methods. Our approach is also competitive with total variation regularization both in terms of MSE and computation time. We show that lscr¹ regularization allows partial recovery of the missing k-space regions. We also present a multi-level version that significantly reduces the computational cost.