摘要翻译：
利用$L_1$正则化来求一个欠定线性系统的稀疏解。由于稀疏信号在遥感中的广泛应用，这种正则化方法及其扩展在图像融合、目标检测、图像超分辨率等许多遥感问题中得到了广泛的应用，并取得了很好的效果。然而，解决这类稀疏重建问题计算量大，在实际应用中存在局限性。本文提出了一种求解复值$L_1$正则化最小二乘问题的新的高效算法。以高维层析合成孔径雷达（TomoSAR）为例，用仿真数据和实际数据进行了大量实验，结果表明，该方法在保持二阶方法精度的同时，处理速度提高了一到两个数量级。虽然我们选择了TomoSAR作为例子，但所提出的方法可以普遍适用于任何谱估计问题。
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英文标题：
《A fast and accurate basis pursuit denoising algorithm with application
  to super-resolving tomographic SAR》
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作者：
Yilei Shi, Xiao Xiang Zhu, Wotao Yin and Richard Bamler
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Image and Video Processing        图像和视频处理
分类描述：Theory, algorithms, and architectures for the formation, capture, processing, communication, analysis, and display of images, video, and multidimensional signals in a wide variety of applications. Topics of interest include: mathematical, statistical, and perceptual image and video modeling and representation; linear and nonlinear filtering, de-blurring, enhancement, restoration, and reconstruction from degraded, low-resolution or tomographic data; lossless and lossy compression and coding; segmentation, alignment, and recognition; image rendering, visualization, and printing; computational imaging, including ultrasound, tomographic and magnetic resonance imaging; and image and video analysis, synthesis, storage, search and retrieval.
用于图像、视频和多维信号的形成、捕获、处理、通信、分析和显示的理论、算法和体系结构。感兴趣的主题包括：数学，统计，和感知图像和视频建模和表示；线性和非线性滤波、去模糊、增强、恢复和重建退化、低分辨率或层析数据；无损和有损压缩编码；分割、对齐和识别；图像渲染、可视化和打印；计算成像，包括超声、断层和磁共振成像；以及图像和视频的分析、合成、存储、搜索和检索。
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英文摘要：
  $L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many remote sensing problems, such as image fusion, target detection, image super-resolution, and others and have led to promising results. However, solving such sparse reconstruction problems is computationally expensive and has limitations in its practical use. In this paper, we proposed a novel efficient algorithm for solving the complex-valued $L_1$ regularized least squares problem. Taking the high-dimensional tomographic synthetic aperture radar (TomoSAR) as a practical example, we carried out extensive experiments, both with simulation data and real data, to demonstrate that the proposed approach can retain the accuracy of second order methods while dramatically speeding up the processing by one or two orders. Although we have chosen TomoSAR as the example, the proposed method can be generally applied to any spectral estimation problems.
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PDF链接：
https://arxiv.org/pdf/1805.01759