Abstract
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.
Abstract (translated)
深度学习近年来成功地应用于图像压缩感知(CS)中。然而，现有的网络方法往往被训练为黑盒，缺乏先前知识往往成为进一步性能改进的瓶颈。为了克服这一缺点，本文提出了一种使用非局部先前的新型CS方法，该方法将传统的优化方法的解释性与网络方法的速度相结合，称为NL-CSNet。我们从扩展拉格朗日方法的迭代中展开每个阶段，以解决非局部和稀疏 Regularized 优化问题，通过网络实现。NL-CSNet由采样模块和恢复模块组成。在采样模块中，我们使用可学习采样矩阵而不是预先定义的矩阵。在恢复模块中，采用点 wise的非局部网络来捕捉长距离特征对应关系。参与重要参数(例如采样矩阵、非线性变换、收缩阈值、步长大小等)的学习是端到端学习的，而不是手工构建的。此外，为了促进实际实现，同时采用Orthogonal 和二进制采样矩阵约束。对自然图像和磁共振成像(MRI)进行了广泛的实验，证明了该方法在保持极大的解释性和速度优势的同时，击败了最先进的方法。
URL
https://arxiv.org/abs/2305.03899
