Regularization#
Beyond the acceleration factor the coil geometry supports, the SENSE problem is ill-conditioned: a least-squares solution amplifies noise, and the aliasing of the undersampling is not fully resolved. A regularized reconstruction adds prior knowledge of the image as a penalty. This section compares Tikhonov, wavelet-sparsity (compressed sensing) and total-variation penalties on one undersampled acquisition and shows how the regularization weight is chosen. It then writes the same reconstruction as an explicit encoding operator and an iterative solver, the form required by an encoding for which BART has no application. Inverse problems and their solvers introduces the formulations and the algorithms.
