Dual-grid parameter choice method with application to image deblurring

Abstract

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice remains an open question in general. A novel approach for parameter choice is introduced, based on the use of two slightly different computational models for the same inverse problem. Small parameter values should give two very different reconstructions due to amplification of noise. Large parameter values lead to two identical but trivial reconstructions. Optimal parameter is chosen between the extremes by matching image similarity of the two reconstructions with a pre-defined value. Efficacy of the new method is demonstrated with image deblurring using measured data and two different regularizers.

29 pages, 20 figures, 3 tables

References in corpus (6)

• Bilevel parameter learning for higher-order total variation regularisation models
• Regularization independent of the noise level: an analysis of quasi-optimality
• Beyond the Bakushinskii veto: Regularising linear inverse problems without knowing the noise distribution
• Controlled Wavelet Domain Sparsity in X-ray Tomography
• Linearly convergent bilevel optimization with single-step inner methods
• Dyadic partition-based training schemes for TV/TGV denoising