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This paper introduces a data-driven smooth-to-hard spectral regularization method for general linear inverse problems, leveraging an explicit saturating spectral penalty. The method's inherent weak convexity guarantees a unique scaled update and proximal-gradient stationarity, with independent validation enabling finite-grid parameter selection. Demonstrated on MRI reconstruction, this approach offers robust and controllable regularization for ill-posed inverse problems.
A novel smooth-to-hard spectral regularizer achieves guaranteed proximal-gradient stationarity and efficient parameter selection for linear inverse problems.
The logistic smooth-to-hard shrinker is the proximal map of an explicit saturating spectral penalty for general linear inverse problems. Its exact weak convexity yields a unique scaled update and proximal-gradient stationarity guarantees, while independent validation provides finite-grid parameter-selection control. We use MRI as an illustrative example.