Training Adaptive Reconstruction Networks for Blind Inverse Problems
This addresses the adaptivity issue in physics-informed neural networks for inverse problems, which is incremental but important for real-world applications like medical imaging.
The paper tackles the problem of neural networks failing to generalize to different forward operators in inverse problems by training them on a family of operators, achieving reconstruction quality without significant compromise across applications like MRI, CT, and image deblurring.
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.