Whiteness-based bilevel learning of regularization parameters in imaging
This addresses the challenge of parameter tuning in imaging for researchers and practitioners, offering an unsupervised alternative to supervised methods, though it is incremental as it builds on existing bilevel optimization and whiteness metrics.
The paper tackles the problem of learning regularization parameters for imaging inverse problems with additive white Gaussian noise without needing ground-truth data, by optimizing the whiteness of the residual, and shows that this approach yields estimates close to oracle and discrepancy-based methods in Total Variation-regularized image deconvolution.
We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics relying either on the prior knowledge of reference data and/or on some (partial) knowledge on the noise statistics, the proposed approach optimizes the whiteness of the residual between the observed data and the observation model with no need of ground-truth data.We validate the approach on standard Total Variation-regularized image deconvolution problems which show that the proposed quality metric provides estimates close to the mean-square error oracle and to discrepancy-based principles.