The adaptive least squares restoration method presented in this paper is based on three fundamental properties. First, the regularization operator should be selected such that it removes the correlation contained in the original signal as far as possible. Therefore it should approximate a whitening filter as close as possible. Second, the function which provides the locally adaptive weighting of the degree of regularization must be matched to the regularization operator. Third, a suitable weighting of the noise term depending on the reliability of the measured data is introduced. The weighting function can also be used to incorporate the solution of the boundary problem as well as of the resampling problem directly into the restoration. The resulting adaptive restoration method leads to proper suppression of noise as well as of oscillations without strong blurring of discontinuities. The whitening operators can be calculated approximately from the data at hand and we do not have to select a particular regularization operator in advance.
Acknowledgments
A special acknowledgment is due to Prof. Leonid P. Yaroslavsky from the Russian Academy of Sciences who provided the basic idea to use whitening filters as regularization operators in adaptive least squares restoration.