压缩感知理论可以被用于解决信源采集设备计算资源受限的问题，但信号重构过程存在不确定性。传统的重构算法计算复杂度高，难以在实际中应用。近期，基于深度学习的重构算法打破传统算法的局限性，以其速度快、质量高等特点受到了广泛关注。现有的深度学习重构算法可以划分为“黑盒子”以及基于优化启发网络两种类型。与“黑盒子”式的网络结构相比，基于优化启发的深度网络更容易获得高精度的恢复，同时也更具可解释性。然而现有基于优化启发的图像压缩感知重构网络在每个优化阶段仅学习单一梯度，存在测量值信息利用不足、难以准确地学习梯度等缺点，限制了重构性能的提升。为了更充分地利用测量值信息，降低梯度学习的难度，本文提出了高维空间梯度学习思想，实现更准确的梯度回归。在此基础上，本文提出了特征域近端高维梯度下降（FPHGD）算法，并设计了实现该算法的深度神经网络（FPHGD-Net）以获得高精度图像重构结果。此外，本文设计了3种不同复杂度的深度空间近端映射网络结构，以满足不同的应用条件，按空间复杂度从低到高，相应模型分别为FPHGD-Net-Tiny、FPHGD-Net、FPHGD-Net-Plus。实验结果表明，与OPINE-Net+相比，所提3种模型在Set11数据上的平均PSNR分别提升1.34、1.51和1.88 dB，并且在重构视觉效果上，能够恢复出更丰富的图像细节。

Compressed sensing theory can be used to solve the problem of limited computing resources of information source acquisition equipment, but there is uncertainty in the signal reconstruction process. Traditional reconstruction algorithm is difficult to be applied in practice because of its high computational complexity. Recently, the reconstruction algorithm based on deep learning has broken the limitation of traditional algorithms, and has attracted wide attention with its fast reconstruction speed and high quality. Existing deep learning reconstruction algorithms can be divided into two types: “black box” and optimization-based inspired network. Compared with the “black box” network structure, the optimization-inspired deep network is easier to obtain high-precision recovery and more interpretable. However, the existing image compressed sensing reconstruction optimization-inspired networks only learn a single gradient in each optimization phase and has shortcomings such as insufficient use of measured information and difficulty in learning gradients, limiting the improvement of reconstruction performance. In order to make full use of the measurement and reduce the difficulty of gradient learning, the idea of high-dimensional space gradient learning was proposed to achieve more accurate gradient regression. On this basis, this paper proposed Feature-domain Proximal High-Dimensional Gradient Descent (FPHGD) algorithm, and designed a Feature-domain Proximal High-dimensional Gradient Descent Network (FPHGD-Net) to realize this algorithm, so as to obtain high-precision image reconstruction. In addition, three kinds of deep space proximal mapping network structures with different complexity were designed to meet different application. According to the spatial complexity from low to high, the corresponding models are respectively called FPHGD-Net-Tiny, FPHGD-Net and FPHGD-Net-Plus. Extensive experiment shows that, compared with OPINE-Net+, the average PSNR of the three proposed models on Set11 increase 1.34, 1.51 and 1.88 dB, and recover richer image details in the reconstruction of visual effects.