Deep learning has been applied to compressive sensing (CS) of images
successfully in recent years. However, existing network-based methods are often
trained as the black box, in which the lack of prior knowledge is often the
bottleneck for further performance improvement. To overcome this drawback, this
paper proposes a novel CS method using non-local prior which combines the
interpretability of the traditional optimization methods with the speed of
network-based methods, called NL-CS Net. We unroll each phase from iteration of
the augmented Lagrangian method solving non-local and sparse regularized
optimization problem by a network. NL-CS Net is composed of the up-sampling
module and the recovery module. In the up-sampling module, we use learnable
up-sampling matrix instead of a predefined one. In the recovery module,
patch-wise non-local network is employed to capture long-range feature
correspondences. Important parameters involved (e.g. sampling matrix, nonlinear
transforms, shrinkage thresholds, step size, $etc.$) are learned end-to-end,
rather than hand-crafted. Furthermore, to facilitate practical implementation,
orthogonal and binary constraints on the sampling matrix are simultaneously
adopted. Extensive experiments on natural images and magnetic resonance imaging
(MRI) demonstrate that the proposed method outperforms the state-of-the-art
methods while maintaining great interpretability and speed.

本文提出了一种使用非局部先验的 CS 方法，称为 NL-CS Net，通过学习解决非局部和稀疏正则化优化问题的扩展 Lagrangian 方法的每个阶段来解决现有网络方法的不足，其中重要参数是端对端学习的，并且在自然图像和磁共振成像实验中表现出更好的性能。