Inspired by certain optimization solvers, the deep unfolding network (DUN) has attracted much attention in recent years for image compressed sensing (CS). However, there still exist the following two issues: 1) In existing DUNs, most hyperparameters are usually content independent, which greatly limits their adaptability for different input contents. 2) In each iteration, a plain convolutional neural network is usually adopted, which weakens the perception of wider context prior and therefore depresses the expressive ability. In this paper, inspired by the traditional Proximal Gradient Descent (PGD) algorithm, a novel DUN for image compressed sensing (dubbed DUN-CSNet) is proposed to solve the above two issues. Specifically, for the first issue, a novel content adaptive gradient descent network is proposed, in which a well-designed step size generation sub-network is developed to dynamically allocate the corresponding step sizes for different textures of input image by generating a content-aware step size map, realizing a content-adaptive gradient updating. For the second issue, considering the fact that many similar patches exist in an image but have undergone a deformation, a novel deformation-invariant non-local proximal mapping network is developed, which can adaptively build the long-range dependencies between the nonlocal patches by deformation-invariant non-local modeling, leading to a wider perception on context priors. Extensive experiments manifest that the proposed DUN-CSNet outperforms existing state-of-the-art CS methods by large margins.

翻译：受某些优化求解器的启发，深度展开网络（DUN）近年来在图像压缩感知（CS）领域备受关注。然而，仍存在以下两个问题：1）现有深度展开网络中的大多数超参数通常与内容无关，这严重限制了其对不同输入内容的适应性；2）每次迭代中通常采用普通卷积神经网络，这削弱了对更广泛上下文先验的感知能力，从而降低了表达能力。本文受经典近端梯度下降（PGD）算法启发，提出一种新型图像压缩感知深度展开网络（记为DUN-CSNet）以解决上述问题。具体而言，针对第一个问题，提出一种新型内容自适应梯度下降网络，其中设计了一个精密的步长生成子网络，通过生成内容感知步长图为输入图像的不同纹理动态分配对应步长，实现内容自适应梯度更新。针对第二个问题，考虑到图像中存在大量经过形变的相似图像块，开发了一种新型变形不变非局部近端映射网络，能够通过变形不变非局部建模自适应构建非局部块间的长程依赖关系，从而获得更广泛的上下文先验感知。大量实验表明，所提DUN-CSNet以显著优势超越现有最先进的压缩感知方法。