With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional optimization-based methods and the speed of recent network-based ones. Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general 1 norm CS reconstruction model. To cast ISTA into deep network form, we develop an effective strategy to solve the proximal mapping associated with the sparsity-inducing regularizer using nonlinear transforms. All the parameters in ISTA-Net (e.g. nonlinear transforms, shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than being hand-crafted. Moreover, considering that the residuals of natural images are more compressible, an enhanced version of ISTA-Net in the residual domain, dubbed ISTA-Net + , is derived to further improve CS reconstruction. Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and networkbased CS methods by large margins, while maintaining fast computational speed. Our source codes are available: http://jianzhang.tech/projects/ISTA-Net.

将优化算法映射到神经网络中，深度展开的网络（DUNS）在压缩传感（CS）方面取得了令人印象深刻的成功。从优化的角度来看，Duns从迭代步骤中继承了一个明确且可解释的结构。但是，从神经网络设计的角度来看，大多数现有的Dun是基于传统图像域展开而固有地建立的，该图像域的展开将一通道图像作为相邻阶段之间的输入和输出，从而导致信息传输能力不足，并且不可避免地会损失图像。细节。在本文中，为了打破上述瓶颈，我们首先提出了一个广义的双域优化框架，该框架是逆成像的一般性，并将（1）图像域和（2）卷积编码域先验的优点整合到限制解决方案空间中的可行区域。通过将所提出的框架展开到深神经网络中，我们进一步设计了一种新型的双域深卷积编码网络（D3C2-NET），用于CS成像，具有通过所有展开的阶段传输高通量特征级图像表示的能力。关于自然图像和MR图像的实验表明，与其他最先进的艺术相比，我们的D3C2-NET实现更高的性能和更好的准确性权衡权衡。

通过将某些优化求解器与深神经网络相结合，深层展开网络（DUN）近年来引起了图像压缩感（CS）的广泛关注。但是，现有DUN中仍然存在几个问题：1）对于每次迭代，通常采用一个简单的堆叠卷积网络，这显然限制了这些模型的表现力。 2）培训完成后，对于任何输入内容，大多数现有DUNS的超参数均已固定，这大大削弱了其适应性。在本文中，通过展开快速迭代的收缩阈值算法（FISTA），提出了一种新颖的快速分层dun，被称为Fhdun，用于图像压缩传感，开发出了精心设计的层次结构，以合作探索富人的上下文，以探索富人的上下文。多尺度空间中的信息。为了进一步增强适应性，在我们的框架中开发了一系列的超参数生成网络，以根据输入内容动态生产相应的最佳超参数。此外，由于Fista的加速政策，新嵌入的加速模块使拟议的Fhdun节省了超过50％的迭代循环，以抵抗最近的Duns。广泛的CS实验表明，所提出的FHDUN优于现有的最新CS方法，同时保持较少的迭代。

为了更有效地解决图像压缩传感（CS）问题，我们提出了一种新颖的内容可扩展的网络，该网络称为CASNET，该网络共同实现了自适应采样率分配，精细的粒状可伸缩性和高质量的重建。我们首先采用数据驱动的显着性检测器来评估不同图像区域的重要性，并提出基于显着性的块比率汇总（BRA）策略来分配采样率。然后开发一个统一的可学习生成矩阵，以产生具有有序结构的任何CS比的采样矩阵。 CASNET配备了由显着性信息和防止伪影的多块训练方案引导的优化启发的恢复子网，CASNET与一个单个模型共同重建以各种采样率采样的图像阻止。为了加速训练收敛并改善网络鲁棒性，我们提出了一种基于SVD的初始化方案和随机转换增强（RTE）策略，在没有引入额外参数的情况下是可扩展的。所有CASNET组件都可以组合和端到端学习。我们进一步提供了四个阶段的实施，用于评估和实际部署。实验表明，CASNET大量优于其他CS网络，从而验证了其组件和策略之间的协作和相互支持。代码可在https://github.com/guaishou74851/casnet上找到。

我们提出了一个基于一般学习的框架，用于解决非平滑和非凸图像重建问题。我们将正则函数建模为$ l_ {2,1} $ norm的组成，并将平滑但非convex功能映射参数化为深卷积神经网络。我们通过利用Nesterov的平滑技术和残留学习的概念来开发一种可证明的趋同的下降型算法来解决非平滑非概念最小化问题，并学习网络参数，以使算法的输出与培训数据中的参考匹配。我们的方法用途广泛，因为人们可以将各种现代网络结构用于正规化，而所得网络继承了算法的保证收敛性。我们还表明，所提出的网络是参数有效的，其性能与实践中各种图像重建问题中的最新方法相比有利。

基于深度网络的图像压缩感（CS）近年来引起了很多关注。然而，现有的基于深网络的CS方案以逐个块的方式重建目标图像，其导致严重的块伪像或将深网络训练为黑盒，其带来了对图像先验知识的有限识别。本文提出了一种使用非局部神经网络（NL-CSNet）的新型图像CS框架，其利用具有深度网络的非本地自相似子，提高重建质量。在所提出的NL-CSNET中，构造了两个非本地子网，用于分别利用测量域中的非本地自相似子系统和多尺度特征域。具体地，在测量域的子网中，建立用于更好的初始重建的不同图像块的测量之间的长距离依赖性。类似地，在多尺度特征域的子网中，在深度重建的多尺度空间中探讨了密集特征表示之间的亲和力。此外，开发了一种新的损失函数以增强非本地表示之间的耦合，这也能够实现NL-CSNet的端到端训练。广泛的实验表明，NL-CSNet优于现有的最先进的CS方法，同时保持快速的计算速度。

卷积神经网络（CNNS）成功地进行了压缩图像感测。然而，由于局部性和重量共享的归纳偏差，卷积操作证明了建模远程依赖性的内在限制。变压器，最初作为序列到序列模型设计，在捕获由于基于自我关注的架构而捕获的全局背景中，即使它可以配备有限的本地化能力。本文提出了一种混合框架，一个混合框架，其集成了从CNN提供的借用的优点以及变压器提供的全局上下文，以获得增强的表示学习。所提出的方法是由自适应采样和恢复组成的端到端压缩图像感测方法。在采样模块中，通过学习的采样矩阵测量图像逐块。在重建阶段，将测量投射到双杆中。一个是用于通过卷积建模邻域关系的CNN杆，另一个是用于采用全球自我关注机制的变压器杆。双分支结构是并发，并且本地特征和全局表示在不同的分辨率下融合，以最大化功能的互补性。此外，我们探索一个渐进的战略和基于窗口的变压器块，以降低参数和计算复杂性。实验结果表明了基于专用变压器的架构进行压缩感测的有效性，与不同数据集的最先进方法相比，实现了卓越的性能。

Deep unfolding networks (DUNs) have proven to be a viable approach to compressive sensing (CS). In this work, we propose a DUN called low-rank CS network (LR-CSNet) for natural image CS. Real-world image patches are often well-represented by low-rank approximations. LR-CSNet exploits this property by adding a low-rank prior to the CS optimization task. We derive a corresponding iterative optimization procedure using variable splitting, which is then translated to a new DUN architecture. The architecture uses low-rank generation modules (LRGMs), which learn low-rank matrix factorizations, as well as gradient descent and proximal mappings (GDPMs), which are proposed to extract high-frequency features to refine image details. In addition, the deep features generated at each reconstruction stage in the DUN are transferred between stages to boost the performance. Our extensive experiments on three widely considered datasets demonstrate the promising performance of LR-CSNet compared to state-of-the-art methods in natural image CS.

高光谱成像是各种应用的基本成像模型，尤其是遥感，农业和医学。灵感来自现有的高光谱相机，可以慢，昂贵或笨重，从低预算快照测量中重建高光谱图像（HSIS）已经绘制了广泛的关注。通过将截断的数值优化算法映射到具有固定数量的相位的网络中，近期深度展开网络（DUNS）用于光谱快照压缩感应（SCI）已经取得了显着的成功。然而，DUNS远未通过缺乏交叉相位相互作用和适应性参数调整来达到有限的工业应用范围。在本文中，我们提出了一种新的高光谱可分解的重建和最佳采样深度网络，用于SCI，被称为HeroSnet，其中包括在ISTA展开框架下的几个阶段。每个阶段可以灵活地模拟感测矩阵，并在梯度下降步骤中进行上下文调整步骤，以及分层熔断器，并在近侧映射步骤中有效地恢复当前HSI帧的隐藏状态。同时，终端实现硬件友好的最佳二进制掩模，以进一步提高重建性能。最后，我们的Herosnet被验证以优于大幅边缘的模拟和实际数据集的最先进的方法。

在图像压缩传感（CS）中将深层神经网络纳入了最近在多媒体技术和应用中的密集关注。随着深网接近，直接从CS测量中了解了反映射，重建速度的速度明显快于常规CS算法。但是，对于现有的基于网络的方法，CS采样过程必须映射单独的网络模型。由于封锁伪像，这可能会降低图像CS的性能，尤其是当将多个采样率分配给图像中的不同块时。在本文中，我们通过利用与性能显着超过当前最新方法的间隔相关性来开发一个用于基于块的图像CS的多通道深网。显着的性能改善归因于块近似，但完全去除了封闭伪像的图像。具体而言，使用我们的多通道结构，可以在单个模型中重建具有多种采样率的图像块。然后，最初重建的块能够将其重新组装成完整的图像中，以通过展开基于手动设计的基于手动设计的CS恢复算法来改善恢复的图像。实验结果表明，所提出的方法在客观指标和主观视觉图像质量方面优于最先进的CS方法。我们的源代码可从https://github.com/siwangzhou/deepbcs获得。

Compressive Sensing (CS) is an effective approach for fast Magnetic Resonance Imaging (MRI). It aims at reconstructing MR image from a small number of undersampled data in k-space, and accelerating the data acquisition in MRI. To improve the current MRI system in reconstruction accuracy and computational speed, in this paper, we propose a novel deep architecture, dubbed ADMM-Net. ADMM-Net is defined over a data flow graph, which is derived from the iterative procedures in Alternating Direction Method of Multipliers (ADMM) algorithm for optimizing a CS-based MRI model. In the training phase, all parameters of the net, e.g., image transforms, shrinkage functions, etc., are discriminatively trained end-to-end using L-BFGS algorithm. In the testing phase, it has computational overhead similar to ADMM but uses optimized parameters learned from the training data for CS-based reconstruction task. Experiments on MRI image reconstruction under different sampling ratios in k-space demonstrate that it significantly improves the baseline ADMM algorithm and achieves high reconstruction accuracies with fast computational speed.

Deep neural networks provide unprecedented performance gains in many real world problems in signal and image processing. Despite these gains, future development and practical deployment of deep networks is hindered by their blackbox nature, i.e., lack of interpretability, and by the need for very large training sets. An emerging technique called algorithm unrolling or unfolding offers promise in eliminating these issues by providing a concrete and systematic connection between iterative algorithms that are used widely in signal processing and deep neural networks. Unrolling methods were first proposed to develop fast neural network approximations for sparse coding. More recently, this direction has attracted enormous attention and is rapidly growing both in theoretic investigations and practical applications. The growing popularity of unrolled deep networks is due in part to their potential in developing efficient, high-performance and yet interpretable network architectures from reasonable size training sets. In this article, we review algorithm unrolling for signal and image processing. We extensively cover popular techniques for algorithm unrolling in various domains of signal and image processing including imaging, vision and recognition, and speech processing. By reviewing previous works, we reveal the connections between iterative algorithms and neural networks and present recent theoretical results. Finally, we provide a discussion on current limitations of unrolling and suggest possible future research directions.

磁共振（MR）图像重建来自高度缺点$ K $ -space数据在加速MR成像（MRI）技术中至关重要。近年来，基于深度学习的方法在这项任务中表现出很大的潜力。本文提出了一种学习的MR图像重建半二次分割算法，并在展开的深度学习网络架构中实现算法。我们比较我们提出的方法对针对DC-CNN和LPDNET的公共心先生数据集的性能，我们的方法在定量结果和定性结果中表现出其他方法，具有更少的模型参数和更快的重建速度。最后，我们扩大了我们的模型，实现了卓越的重建质量，并且改善为1.76美元$ 276 $ 274美元的LPDNET以5美元\倍率为5美元的峰值信噪比。我们的方法的代码在https://github.com/hellopipu/hqs-net上公开使用。

与传统CS方法相比，基于深度学习（DL）的压缩传感（CS）已被应用于图像重建的更好性能。但是，大多数现有的DL方法都利用逐个块测量，每个测量块分别恢复，这引入了重建的有害阻塞效应。此外，这些方法的神经元接受场被设计为每一层的大小相同，这只能收集单尺度的空间信息，并对重建过程产生负面影响。本文提出了一个新的框架，称为CS测量和重建的多尺度扩张卷积神经网络（MSDCNN）。在测量期间，我们直接从训练有素的测量网络中获得所有测量，该测量网络采用了完全卷积结构，并通过输入图像与重建网络共同训练。它不必将其切成块，从而有效地避免了块效应。在重建期间，我们提出了多尺度特征提取（MFE）体系结构，以模仿人类视觉系统以捕获同一功能映射的多尺度特征，从而增强了框架的图像特征提取能力并提高了框架的性能并提高了框架的性能。影像重建。在MFE中，有多个并行卷积通道以获取多尺度特征信息。然后，将多尺度功能信息融合在一起，并以高质量重建原始图像。我们的实验结果表明，根据PSNR和SSIM，该提出的方法对最新方法的性能有利。

最近，一些研究在图像压缩感测（CS）任务中应用了深层卷积神经网络（CNN），以提高重建质量。但是，卷积层通常具有一个小的接受场。因此，使用CNN捕获远程像素相关性是具有挑战性的，这限制了其在Image CS任务中的重建性能。考虑到这一限制，我们为图像CS任务（称为uformer-ics）提出了一个U形变压器。我们通过将CS的先验投影知识集成到原始变压器块中，然后使用基于投影基于投影的变压器块和残留卷积块构建对称重建模型来开发一个基于投影的变压器块。与以前的基于CNN的CS方法相比，只能利用本地图像特征，建议的重建模型可以同时利用图像的局部特征和远程依赖性，以及CS理论的先前投影知识。此外，我们设计了一个自适应采样模型，该模型可以基于块稀疏性自适应采样图像块，这可以确保压缩结果保留在固定采样比下原始图像的最大可能信息。提出的UFORFORFOR-ICS是一个端到端框架，同时学习采样和重建过程。实验结果表明，与现有的基于深度学习的CS方法相比，它的重建性能明显优于重建性能。

Most Deep Learning (DL) based Compressed Sensing (DCS) algorithms adopt a single neural network for signal reconstruction, and fail to jointly consider the influences of the sampling operation for reconstruction. In this paper, we propose unified framework, which jointly considers the sampling and reconstruction process for image compressive sensing based on well-designed cascade neural networks. Two sub-networks, which are the sampling sub-network and the reconstruction sub-network, are included in the proposed framework. In the sampling sub-network, an adaptive full connected layer instead of the traditional random matrix is used to mimic the sampling operator. In the reconstruction sub-network, a cascade network combining stacked denoising autoencoder (SDA) and convolutional neural network (CNN) is designed to reconstruct signals. The SDA is used to solve the signal mapping problem and the signals are initially reconstructed. Furthermore, CNN is used to fully recover the structure and texture features of the image to obtain better reconstruction performance. Extensive experiments show that this framework outperforms many other state-of-the-art methods, especially at low sampling rates.

Tomographic SAR technique has attracted remarkable interest for its ability of three-dimensional resolving along the elevation direction via a stack of SAR images collected from different cross-track angles. The emerged compressed sensing (CS)-based algorithms have been introduced into TomoSAR considering its super-resolution ability with limited samples. However, the conventional CS-based methods suffer from several drawbacks, including weak noise resistance, high computational complexity, and complex parameter fine-tuning. Aiming at efficient TomoSAR imaging, this paper proposes a novel efficient sparse unfolding network based on the analytic learned iterative shrinkage thresholding algorithm (ALISTA) architecture with adaptive threshold, named Adaptive Threshold ALISTA-based Sparse Imaging Network (ATASI-Net). The weight matrix in each layer of ATASI-Net is pre-computed as the solution of an off-line optimization problem, leaving only two scalar parameters to be learned from data, which significantly simplifies the training stage. In addition, adaptive threshold is introduced for each azimuth-range pixel, enabling the threshold shrinkage to be not only layer-varied but also element-wise. Moreover, the final learned thresholds can be visualized and combined with the SAR image semantics for mutual feedback. Finally, extensive experiments on simulated and real data are carried out to demonstrate the effectiveness and efficiency of the proposed method.

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. In recent years, model-based deep learning methods that combine imaging physics with learned regularization priors have been emerging as more powerful alternatives for image recovery. The main focus of this paper is to introduce a memory efficient model-based algorithm with similar theoretical guarantees as CS methods. The proposed iterative algorithm alternates between a gradient descent involving the score function and a conjugate gradient algorithm to encourage data consistency. The score function is modeled as a monotone convolutional neural network. Our analysis shows that the monotone constraint is necessary and sufficient to enforce the uniqueness of the fixed point in arbitrary inverse problems. In addition, it also guarantees the convergence to a fixed point, which is robust to input perturbations. Current algorithms including RED and MoDL are special cases of the proposed algorithm; the proposed theoretical tools enable the optimization of the framework for the deep equilibrium setting. The proposed deep equilibrium formulation is significantly more memory efficient than unrolled methods, which allows us to apply it to 3D or 2D+time problems that current unrolled algorithms cannot handle.

Neural networks have recently allowed solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these networks suffer from a major defect: when trained on a given forward operator, they do not generalize well to a different one. The aim of this paper is twofold. First, we show through various applications that training the network with a family of forward operators allows solving the adaptivity problem without compromising the reconstruction quality significantly. Second, we illustrate that this training procedure allows tackling challenging blind inverse problems. Our experiments include partial Fourier sampling problems arising in magnetic resonance imaging (MRI), computerized tomography (CT) and image deblurring.

基于分数的扩散模型为使用数据分布的梯度建模图像提供了一种强大的方法。利用学到的分数函数为先验，在这里，我们引入了一种从条件分布中进行测量的方法，以便可以轻松地用于求解成像中的反问题，尤其是用于加速MRI。简而言之，我们通过denoising得分匹配来训练连续的时间依赖分数函数。然后，在推论阶段，我们在数值SDE求解器和数据一致性投影步骤之间进行迭代以实现重建。我们的模型仅需要用于训练的幅度图像，但能够重建复杂值数据，甚至扩展到并行成像。所提出的方法是不可知论到子采样模式，可以与任何采样方案一起使用。同样，由于其生成性质，我们的方法可以量化不确定性，这是标准回归设置不可能的。最重要的是，我们的方法还具有非常强大的性能，甚至击败了经过全面监督训练的模型。通过广泛的实验，我们在质量和实用性方面验证了我们方法的优势。