Data-Consistent Learning of Inverse Problems

TL;DR

This paper introduces a data-consistent neural network approach for inverse problems that combines classical regularization with deep learning, ensuring both theoretical guarantees and high-quality reconstructions.

Contribution

It proposes null-space networks integrated with classical regularization to create a convergent, data-consistent learning method for inverse problems.

Findings

Ensures stability and convergence through measurement model enforcement.

Produces reconstructions that are both accurate and visually appealing.

Bridges classical regularization with deep learning for inverse problems.

Abstract

Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced flexibility or visual quality. Learned reconstruction methods, such as convolutional neural networks, can produce visually compelling results, yet they typically lack rigorous theoretical guarantees. DC (DC) networks address this gap by enforcing the measurement model within the network architecture. In particular, null-space networks combined with a classical regularization method as an initial reconstruction define a convergent regularization method. This approach preserves the theoretical reliability of classical schemes while leveraging the expressive power of data-driven learning, yielding reconstructions that are both accurate and visually appealing.