A parameter‐choice method that exploits residual information

Abstract

Most algorithms for choosing the regularization parameter in a discrete ill‐posed problem are based on the norm of the residual vector. In this work we propose a different approach that seeks to use all the information available in the residual vector, and we show how to use statistical tools and fast Fourier transforms to extract this information efficiently. This approach leads to a computationally inexpensive parameter‐choice rule based on the normalized cumulative periodogram, which is particularly suited for large‐scale problems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)