Bilevel parameter learning for higher-order total variation regularisation models
This work addresses parameter tuning challenges in image processing for researchers and practitioners, but it is incremental as it builds on existing bilevel optimization and total variation methods.
The authors tackled the problem of parameter learning in higher-order total variation image reconstruction models by proposing a bilevel optimization approach with an alternative Huber-regularized cost functional, resulting in improved performance and a detailed comparison between TGV^2 and ICTV regularizers based on image structure and noise level.
We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost, based on a Huber regularised TV-seminorm. Differentiability properties of the solution operator are verified and a first-order optimality system is derived. Based on the adjoint information, a quasi-Newton algorithm is proposed for the numerical solution of the bilevel problems. Numerical experiments are carried out to show the suitability of our approach and the improved performance of the new cost functional. Thanks to the bilevel optimisation framework, also a detailed comparison between TGV$^2$ and ICTV is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.