DREAM: Deep-Reparametrization of Adaptive Regularization Maps for Fast Zero-Shot Self-Supervised Learning

Abstract

Adaptive regularization is an effective means of improving the flexibility of classical variational reconstruction methods while retaining their interpretability and mathematical structure. In this work, we propose an approach for learning deep-reparameterized adaptive regularization maps (DREAM) for Total Variation (TV) and Total Generalized Variation (TGV) through algorithm unrolling in a zero-shot, self-supervised setting, requiring no access to large paired datasets. We first validate DREAM on a two-dimensional image-denoising problem and then apply it to large-scale dynamic MRI reconstruction. The resulting adaptive models are theoretically grounded, as they retain the convergence properties of the primal-dual algorithm used as the building block of the unrolled architecture. Our results show that the regularization parameter maps can be learned efficiently, requiring substantially fewer weight updates than state-of-the-art methods to achieve comparable performance. We further demonstrate that the CNN parametrization of the maps acts as an implicit prior and provides effective dimensionality reduction, outperforming direct optimization of the adaptive parameters. Across both applications, the performance gap between supervised and zero-shot training is smaller for DREAM than for the end-to-end deep-learning methods considered for comparison. Remarkably, in dynamic cardiac MRI reconstruction, zero-shot training matches the performance of the supervised model. Moreover, the learned adaptive maps are highly interpretable, providing a compelling alternative to purely deep-learning-based methods when reference data are difficult to obtain.