Smooth or abrupt: a comparison of regularization methods

Daniela Calvetti; Bryan Lewis; Lothar Reichel

doi:10.1117/12.325689

2 October 1998 Smooth or abrupt: a comparison of regularization methods

Daniela Calvetti, Bryan Lewis, Lothar Reichel

Proceedings Volume 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII; (1998) https://doi.org/10.1117/12.325689
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

In this paper we compare a new regularizing scheme based on the exponential filter function with two classical regularizing methods: Tikhonov regularization and a variant of truncated singular value regularization. The filter functions for the former methods are smooth, but for the latter discontinuous. These regularization methods are applied to the restoration of images degraded by blur and noise. The norm of the noise is assumed to be known, and this allows application of the Morozov discrepancy principle to determine the amount of regularization. We compare the restored images produced by the three regularization methods with optimal values of the regularization parameter. This comparison sheds light on how these different approaches are related.

Citation Download Citation

Daniela Calvetti, Bryan Lewis, and Lothar Reichel "Smooth or abrupt: a comparison of regularization methods", Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); https://doi.org/10.1117/12.325689

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