摘要翻译：
使用过完备字典的稀疏表示在各种图像处理任务中都显示出很好的质量结果。字典学习算法使得设计数据自适应字典成为可能，在图像压缩和图像增强方面具有广阔的应用前景。最常见的稀疏字典学习算法分别采用匹配追踪和K-SVD迭代算法进行稀疏编码和字典学习。虽然这种技术产生了很好的效果，但它需要大量的迭代才能收敛到最优解。在本文中，我们使用一种封闭形式稳定的凸优化技术，用于稀疏编码和字典学习。该方法的结果是提供最好的字典和最稀疏的表示，导致最小的重建误差。一旦从压缩感知的样本中重建出图像，我们就使用自适应频率和空间滤波技术来实现精确的图像恢复。实验结果表明，在一定的迭代次数下，该算法比传统的稀疏字典算法具有更好的重建效果。与图像中存在的细节数量相反，该算法以明显较低的迭代次数达到最优解。因此，对于我们的压缩感知框架，使用所提出的算法可以获得高PSNR和低MSE。
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英文标题：
《Reconstruction of Compressively Sensed Images using Convex Tikhonov
  Sparse Dictionary Learning and Adaptive Spectral Filtering》
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作者：
Nishant Deepak Keni, Amol Mangirish Singbal, Rizwan Ahmed
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最新提交年份：
2019
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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：
  Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have promising applications in image compression and image enhancement. The most common sparse dictionary learning algorithms use the techniques of matching pursuit and K-SVD iteratively for sparse coding and dictionary learning respectively. While this technique produces good results, it requires a large number of iterations to converge to an optimal solution. In this article, we use a closed form stabilized convex optimization technique for both sparse coding and dictionary learning. The approach results in providing the best possible dictionary and the sparsest representation resulting in minimum reconstruction error. Once the image is reconstructed from the compressively sensed samples, we use adaptive frequency and spatial filtering techniques to move towards exact image recovery. It is clearly seen from the results that the proposed algorithm provides much better reconstruction results than conventional sparse dictionary techniques for a fixed number of iterations. Depending inversely upon the number of details present in the image, the proposed algorithm reaches the optimal solution with a significantly lower number of iterations. Consequently, high PSNR and low MSE is obtained using the proposed algorithm for our compressive sensing framework.
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PDF链接：
https://arxiv.org/pdf/1801.09135