Alban Gossard

Alban Gossard, Pierre Weiss

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.

Alban Gossard, Frédéric de Gournay, Pierre Weiss

We propose a novel learning based algorithm to generate efficient and physically plausible sampling patterns in MRI. This method has a few advantages compared to recent learning based approaches: i) it works off-the-grid and ii) allows to handle arbitrary physical constraints. These two features allow for much more versatility in the sampling patterns that can take advantage of all the degrees of freedom offered by an MRI scanner. The method consists in a high dimensional optimization of a cost function defined implicitly by an algorithm. We propose various numerical tools to address this numerical challenge.