Generalized Tikhonov Regularization
For general multivariate normal distributions for and the data error, one can apply a transformation of the variables to reduce to the case above. Equivalently, one can seek an to minimize
where we have used to stand for the weighted norm (compare with the Mahalanobis distance). In the Bayesian interpretation is the inverse covariance matrix of, is the expected value of, and is the inverse covariance matrix of . The Tikhonov matrix is then given as a factorization of the matrix (e.g. the Cholesky factorization), and is considered a whitening filter.
This generalized problem can be solved explicitly using the formula
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