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Unformatted text preview: algorithms reduce this noise. In many applications, we need to choose the regularization parameter by au-tomatic methods rather than by eye. If the noise-level is known, then the discrepancy principle is the best: choose the parameter to make the residual Kf g close in norm to the expected norm of the noise. If the noise-level is not known, then generalized cross validation and the L-curve are popular methods. See [1,2] for discussion of such methods.  Per Christian Hansen, James M. Nagy, and Dianne P. OLeary. Deblurring Images: Matrices, Spectra, and Filtering . SIAM Press, Philadelphia, 2006.  Bert W. Rust and Dianne P. OLeary, Residual Periodograms for Choos-ing Regularization Parameters for Ill-Posed Problems, Inverse Problems, 24 (2008) 034005....
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- Fall '11