ABSTRACT
Appropriate use of regularized solutions facilitates minimization of noise build-up without enhancing aliasing artifacts in the reconstruction process. However, the accuracy of regularized output depends on the regularization parameter choice. Chapter 3 discusses different parameter selection strategies in both deterministic and stochastic settings to assign optimal value for the regularization parameter. Typical parameter selection for Tikhonov regularization such as the discrepancy principle, generalized discrepancy principle, unbiased predictive risk estimator (UPRE), Stein’s unbiased risk estimation (SURE), Bayesian approach, generalized cross validation (GCV), quasi-optimality criterion and L-curve are discussed. This is followed by discussions of truncation parameter selection strategies in spectral cut-off regularization. The latter part focuses on regularization parameter selection for sparsity-promoting techniques in the wavelet and finite difference domains. Detailed descriptions of specific selection methods for wavelet regularization such as the Visushrink, SUREshrink, NeighBlock, SUREblock, false discovery rate, Bayesian methods, Ogden’s method and GCV are included. Since the functional form of the TV operator is not well defined, approaches for sparsity promotion in the finite difference domain fall into either a non-linear, partial differential equation–based approach, duality-based approaches or a discrete implementation of the variational formulation. Separate parameter selection approaches in each case are described in detail.
