Data-Consistent Learning of Inverse Problems
This addresses the trade-off between flexibility and reliability in inverse problem reconstruction for fields like medical imaging or signal processing, offering a hybrid solution that is incremental in combining classical and learned methods.
The paper tackled the ill-posed nature of inverse problems by proposing DC networks that enforce measurement models within neural networks, resulting in reconstructions that are both accurate and visually appealing while preserving theoretical guarantees.
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.