The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images. In these applications, DNNs invert a forward operator by finding, via training data, a map between the measurements and the input images. It is then expected that the map is still valid for the test data. This framework, however, introduces measurement inconsistency during testing. We show that such inconsistency, which can be critical in domains like medical imaging or defense, is intimately related to the generalization error. We then propose a framework that post-processes the output of DNNs with an optimization algorithm that enforces measurement consistency. Experiments on MR images show that enforcing measurement consistency via our method can lead to large gains in reconstruction performance.
翻译:深神经网络(DNNs)的显著表现目前使它们成为解决线性反问题的选择方法。 它们已被应用于超级溶解和恢复图像以及重建MR和CT图像。 在这些应用中, DNNs通过培训数据,在测量和输入图像之间找到一张地图,将前方操作器倒转。 然后预计地图对测试数据仍然有效。 但是,这个框架在测试中引入测量不一致。 我们发现,在医学成像或防御等领域至关重要的这种不一致与一般化错误密切相关。 我们然后提出一个框架,在使用优化算法处理DNs输出后,采用优化算法,以强制实现测量一致性。 对 MR 图像的实验表明,通过我们的方法强制测量一致性可以导致重建性能的巨大收益。