Total Deep Variation for Linear Inverse Problems
This addresses image quality issues in computational imaging for researchers and practitioners, though it is incremental as it builds on existing variational and deep learning methods.
The paper tackled linear inverse problems in imaging by proposing a learnable general-purpose regularizer based on deep learning architectures, achieving state-of-the-art performance in image restoration and medical image reconstruction.
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We cast the learning problem as a discrete sampled optimal control problem, for which we derive the adjoint state equations and an optimality condition. By exploiting the variational structure of our approach, we perform a sensitivity analysis with respect to the learned parameters obtained from different training datasets. Moreover, we carry out a nonlinear eigenfunction analysis, which reveals interesting properties of the learned regularizer. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems.