ABSTRACT
Chapter 2 provides an overview of the various existing strategies adopted for regularization wherein a continuous dependence between the measured data and the model parameters is not available. The initial part of this chapter discusses the classification of regularization methods based on the type of priors used. The second half discusses typical regularization methods adopted for MR image reconstruction. This includes different types of regularization in auto-calibrating parallel MRI and CS-MRI for minimization of noise and aliasing artifacts in the reconstruction process. In auto-calibrating parallel MRI, methods to address the poor conditioning of calibration matrix typically include tailored GRAPPA, discrepancy-based adaptive regularization, penalized coefficient regularization, virtual coil approach with different penalizing factors applied to the real and virtual channels, sparsity promoting GRAPPA and Krylov sub-space-based methods. In CS-MRI, on the other hand, the numerical ill-conditioning of the Fourier operator is addressed using sparsity promoting implementations. A brief description of regularization in CS-MRI using redundant representations and their advantages over orthogonal transform domain representations is also included.
