Inverse problems are mathematically ill-posed. Thus, given some (noisy) data, there is more than one solution that fits the data. In recent years, deep neural techniques that find the most appropriate solution, in the sense that it contains a-priori information, were developed. However, they suffer from several shortcomings. First, most techniques cannot guarantee that the solution fits the data at inference. Second, while the derivation of the techniques is inspired by the existence of a valid scalar regularization function, such techniques do not in practice rely on such a function, and therefore veer away from classical variational techniques. In this work we introduce a new family of neural regularizers for the solution of inverse problems. These regularizers are based on a variational formulation and are guaranteed to fit the data. We demonstrate their use on a number of highly ill-posed problems, from image deblurring to limited angle tomography.
翻译:反问题在数学上是不适定的。因此,给定某些(嘈杂的)数据,存在不止一个符合数据的解决方案。近年来,发展了利用深度神经技术寻找最合适解决方案的技术,以便它包含先验信息。然而,它们存在几个缺陷。首先,大多数技术不能保证在推理时解决方案符合数据。其次,虽然技术的导出是受到有效标量正则化函数的存在启发,但这些技术实际上并不依赖于这种函数,因此偏离了传统的变分技术。这项工作介绍了一种用于解决反问题的新型神经正则化器系列。这些正则化器基于变分表达式,保证符合数据。我们在许多高度不适定的问题上展示了它们的用法,从图像去模糊到有限角度层析。