Training Adaptive Reconstruction Networks for Blind Inverse Problems

TL;DR

This paper introduces a training method for neural networks that improves their ability to adapt to different forward operators in inverse problems, enhancing performance in blind scenarios like MRI, CT, and deblurring.

Contribution

The paper proposes training neural networks with a family of forward operators to achieve better adaptivity and handle challenging blind inverse problems without losing reconstruction quality.

Findings

Training with multiple operators improves generalization across different inverse problems.

The method effectively addresses blind inverse problems in MRI, CT, and deblurring.

Experimental results demonstrate significant performance gains in challenging scenarios.

Abstract

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these networks suffer from a major defect: when trained on a given forward operator, they do not generalize well to a different one. The aim of this paper is twofold. First, we show through various applications that training the network with a family of forward operators allows solving the adaptivity problem without compromising the reconstruction quality significantly.Second, we illustrate that this training procedure allows tackling challenging blind inverse problems.Our experiments include partial Fourier sampling problems arising in magnetic resonance imaging (MRI) with sensitivity estimation and off-resonance effects, computerized tomography (CT) with a tilted geometry and image deblurring with Fresnel diffraction kernels.