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.

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.

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。

Deep learning (DL)-based tomographic SAR imaging algorithms are gradually being studied. Typically, they use an unfolding network to mimic the iterative calculation of the classical compressive sensing (CS)-based methods and process each range-azimuth unit individually. However, only one-dimensional features are effectively utilized in this way. The correlation between adjacent resolution units is ignored directly. To address that, we propose a new model-data-driven network to achieve tomoSAR imaging based on multi-dimensional features. Guided by the deep unfolding methodology, a two-dimensional deep unfolding imaging network is constructed. On the basis of it, we add two 2D processing modules, both convolutional encoder-decoder structures, to enhance multi-dimensional features of the imaging scene effectively. Meanwhile, to train the proposed multifeature-based imaging network, we construct a tomoSAR simulation dataset consisting entirely of simulation data of buildings. Experiments verify the effectiveness of the model. Compared with the conventional CS-based FISTA method and DL-based gamma-Net method, the result of our proposed method has better performance on completeness while having decent imaging accuracy.

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。

求解电磁逆散射问题（ISP）由于内在的非线性，呈不良和昂贵的计算成本，挑战。最近，深神经网络（DNN）技术已经成功地应用于ISP上，并在传统方法上示出了优异成像的电位。在本文中，我们分析了DNN溶剂和传统迭代算法之间的类比，并讨论了在训练过程中不能有效地纳入重要的物理现象。我们展示了在DNN的学习过程中包括近端前瞻的重要性。为此，我们提出了新的损耗功能设计，其包括基于多散射的近场数量（例如散射场或感兴趣领域内的诱导电流）。使用各种数值实验研究了物理引导功能的影响。总结了调查的ISP求解器的利弊，综述了不同损失功能。

我们通过基于压缩感测和多输出（MIMO）无线雷达来解决材料缺陷的检测，这些材料缺陷在层状材料结构内部。这里，由于层状结构的表面的反射导致的强杂波通常经常使缺陷挑战的缺陷。因此，需要改进的缺陷检测所需的复杂信号分离方法。在许多情况下，我们感兴趣的缺陷的数量是有限的，并且分层结构的信令响应可以被建模为低秩结构。因此，我们提出了对缺陷检测的关节等级和稀疏最小化。特别是，我们提出了一种基于迭代重量的核和$ \ ell_1- $规范（一种双重重量方法）的非凸法方法，与传统的核规范和$ \ ell_1- $常态最小化相比获得更高的准确性。为此，迭代算法旨在估计低级别和稀疏贡献。此外，我们建议深入学习来学习算法（即，算法展开）的参数，以提高算法的准确性和汇聚速度。我们的数值结果表明，该方法在恢复的低级别和稀疏组分的均方误差和收敛速度方面优于常规方法。

编码的光圈快照光谱成像（CASSI）是一种用于从一个或几个二维投影测量值重建三维高光谱图像（HSI）的技术。但是，较少的投影测量或更多的光谱通道导致了严重的问题，在这种情况下，必须应用正则化方法。为了显着提高重建的准确性，本文提出了一种基于自然图像的稀疏性和深层图像先验（FAMA-SDIP）的快速交流最小化算法。通过将深层图像（DIP）集成到压缩感应（CS）重建原理中，提出的算法可以在没有任何培训数据集的情况下实现最新结果。广泛的实验表明，FAMA-SDIP方法显着优于模拟和实际HSI数据集的主要主要方法。

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.

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。

作为一种引起巨大关注的新兴技术，通过分析继电器表面上的漫反射来重建隐藏物体的非视线（NLOS）成像，具有广泛的应用前景，在自主驾驶，医学成像和医学成像领域防御。尽管信噪比低（SNR）和高不良效率的挑战，但近年来，NLOS成像已迅速发展。大多数当前的NLOS成像技术使用传统的物理模型，通过主动或被动照明构建成像模型，并使用重建算法来恢复隐藏场景。此外，NLOS成像的深度学习算法最近也得到了很多关注。本文介绍了常规和深度学习的NLOS成像技术的全面概述。此外，我们还调查了新的拟议的NLOS场景，并讨论了现有技术的挑战和前景。这样的调查可以帮助读者概述不同类型的NLOS成像，从而加速了在角落周围看到的发展。

我们在凸优化和深度学习的界面上引入了一类新的迭代图像重建算法，以启发凸出和深度学习。该方法包括通过训练深神网络（DNN）作为Denoiser学习先前的图像模型，并将其替换为优化算法的手工近端正则操作员。拟议的airi（``````````````'''''）框架，用于成像复杂的强度结构，并从可见性数据中扩散和微弱的发射，继承了优化的鲁棒性和解释性，以及网络的学习能力和速度。我们的方法取决于三个步骤。首先，我们从光强度图像设计了一个低动态范围训练数据库。其次，我们以从数据的信噪比推断出的噪声水平来训练DNN Denoiser。我们使用训练损失提高了术语，可确保算法收敛，并通过指示进行即时数据库动态范围增强。第三，我们将学习的DeNoiser插入前向后的优化算法中，从而产生了一个简单的迭代结构，该结构与梯度下降的数据输入步骤交替出现Denoising步骤。我们已经验证了SARA家族的清洁，优化算法的AIRI，并经过DNN训练，可以直接从可见性数据中重建图像。仿真结果表明，AIRI与SARA及其基于前卫的版本USARA具有竞争力，同时提供了显着的加速。干净保持更快，但质量较低。端到端DNN提供了进一步的加速，但质量远低于AIRI。

深度学习模型是压缩光谱成像（CSI）恢复的最新模型。这些方法使用深神网络（DNN）作为图像发生器来学习从压缩测量到光谱图像的非线性映射。例如，深频谱先验方法在优化算法中使用卷积自动编码器网络（CAE）通过使用非线性表示来恢复光谱图像。但是，CAE训练与恢复问题分离，这不能保证CSI问题的光谱图像的最佳表示。这项工作提出了联合非线性表示和恢复网络（JR2NET），将表示和恢复任务链接到单个优化问题。 JR2NET由ADMM公式遵循优化启发的网络组成，该网络学习了非线性低维表示，并同时执行通过端到端方法训练的光谱图像恢复。实验结果表明，该方法的优势在PSNR中的改进高达2.57 dB，并且性能比最新方法快2000倍。

Dynamic magnetic resonance image reconstruction from incomplete k-space data has generated great research interest due to its capability to reduce scan time. Never-theless, the reconstruction problem is still challenging due to its ill-posed nature. Recently, diffusion models espe-cially score-based generative models have exhibited great potential in algorithm robustness and usage flexi-bility. Moreover, the unified framework through the variance exploding stochastic differential equation (VE-SDE) is proposed to enable new sampling methods and further extend the capabilities of score-based gener-ative models. Therefore, by taking advantage of the uni-fied framework, we proposed a k-space and image Du-al-Domain collaborative Universal Generative Model (DD-UGM) which combines the score-based prior with low-rank regularization penalty to reconstruct highly under-sampled measurements. More precisely, we extract prior components from both image and k-space domains via a universal generative model and adaptively handle these prior components for faster processing while maintaining good generation quality. Experimental comparisons demonstrated the noise reduction and detail preservation abilities of the proposed method. Much more than that, DD-UGM can reconstruct data of differ-ent frames by only training a single frame image, which reflects the flexibility of the proposed model.

电磁（EM）成像广泛用于感应安全性，生物医学，地球物理学和各种行业。这是一个不当的逆问题，其解决方案通常在计算上昂贵。机器学习（ML）技术，尤其是深度学习（DL）在快速准确的成像中显示出潜力。但是，纯粹的数据驱动方法的高性能依赖于构建与实用方案一致的训练集，而在EM成像任务中通常不可能。因此，普遍性成为主要问题。另一方面，物理原理是EM现象的基础，并为当前的成像技术提供了基准。为了从大数据中的先验知识和物理定律的理论约束中受益，物理学嵌入的ML成像方法已成为近期大量工作的重点。本文调查了各种方案，以将物理学纳入基于学习的EM成像中。我们首先介绍有关逆问题的EM成像和基本公式的背景。然后，我们专注于将物理和ML进行线性和非线性成像组合的三种类型的策略，并讨论它们的优势和局限性。最后，我们在这个快速发展的领域中以公开的挑战和可能的前进方式得出结论。我们的目的是促进将有效，可解释和可控制的智能EM成像方法的研究。

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。

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。

Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and often even discrete optimization task. While the potential of gradient-based learning via the unrolling of iterative recovery algorithms has been demonstrated, it has remained unclear how to leverage this technique when the set of admissible measurement operators is structured and discrete. We tackle this problem by combining unrolled optimization with Gumbel reparametrizations, which enable the computation of low-variance gradient estimates of categorical random variables. Our approach is formalized by GLODISMO (Gradient-based Learning of DIscrete Structured Measurement Operators). This novel method is easy-to-implement, computationally efficient, and extendable due to its compatibility with automatic differentiation. We empirically demonstrate the performance and flexibility of GLODISMO in several prototypical signal recovery applications, verifying that the learned measurement matrices outperform conventional designs based on randomization as well as discrete optimization baselines.

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。

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.