Jodi Mead, Boise State University
2022 AWM Research Symposium
Recent Advancements in Inverse Problems and Imaging

Total Variation (TV) regularization has shown to be effective in recovering parameters with edges or discontinuities. As with any regularization method, regularization parameter selection is important. For example, the discrepancy principle is a classical approach whereby data are fit to a specified tolerance. The tolerance can be identified by noting the least squares data fit follows a χ^2 distribution. However, this approach fails when the number of parameters is greater than or equal to the number of data. Heuristics are then employed to identify the tolerance in the discrepancy principle ,and this leads to oversmoothing. In this work we identify a χ^2 test for TV regularization parameter selection. We prove that the degrees of freedom in the TV regularized residual is the number of data and this is used to identify the appropriate tolerance in a discrepancy principle approach. The importance of this work lies in the fact that the χ^2 test introduced here for TV automates the choice of regularization parameter selection and can straightforwardly be incorporated into any TV algorithm. Results are given for three test images and compared to results using the discrepancy principle and MAP estimates.

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