Residual Periodograms for Choosing Regularization Parameters for Ill-Posed Problems

Published

June 2, 2008

Author(s)

Bert W. Rust, Dianne M. O'Leary

Abstract

Consider an ill-posed problem transformed if necessary so that the errors in the data are independent, identically normally distributed with mean zero and variance 1. We evaluate a method proposed by Rust for choosing the regularization parameter that makes the residuals as close as possible to white noise, using a test based on the cumulative periodogram. We compare this method with standard techniques such as the discrepancy principle, the L-curve, and generalized cross validation, showing that it performs better.

Citation

Inverse Problems

Volume

24

Issue

3

Pub Type

Journals

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Keywords

cumulative periodogram, ill-posed problems, periodogram, regularization

Citation

Rust, B. and O'Leary, D. (2008), Residual Periodograms for Choosing Regularization Parameters for Ill-Posed Problems, Inverse Problems, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=51212 (Accessed October 13, 2025)