图像反卷积的n维卷积性质

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摘要翻译：
卷积系统是线性的、时间不变的，能够描述光学成像过程。基于卷积系统，许多反卷积技术已经发展到光学图像分析中，如提高光学图像的空间分辨率、图像去噪、图像增强等。本文给出了n维卷积的一些性质。利用这些性质，我们提出了图像反卷积方法。该方法利用一系列卷积运算对图像进行解卷。我们证明了该方法具有与现有方法相似的反卷积结果。该方法的核心计算是图像卷积，因此该方法可以很容易地集成到GPU模式下进行大规模的图像反卷积。
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英文标题：
《Properties on n-dimensional convolution for image deconvolution》
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作者：
Song Yizhi, Xu Cheng, Ding Daoxin, Zhou Hang, Quan Tingwei, Li Shiwei
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最新提交年份：
2017
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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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一级分类：Computer Science        计算机科学
二级分类：Computer Vision and Pattern Recognition        计算机视觉与模式识别
分类描述：Covers image processing, computer vision, pattern recognition, and scene understanding. Roughly includes material in ACM Subject Classes I.2.10, I.4, and I.5.
涵盖图像处理、计算机视觉、模式识别和场景理解。大致包括ACM课程I.2.10、I.4和I.5中的材料。
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英文摘要：
  Convolution system is linear and time invariant, and can describe the optical imaging process. Based on convolution system, many deconvolution techniques have been developed for optical image analysis, such as boosting the space resolution of optical images, image denoising, image enhancement and so on. Here, we gave properties on N-dimensional convolution. By using these properties, we proposed image deconvolution method. This method uses a series of convolution operations to deconvolute image. We demonstrated that the method has the similar deconvolution results to the state-of-art method. The core calculation of the proposed method is image convolution, and thus our method can easily be integrated into GPU mode for large-scale image deconvolution.
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PDF链接：
https://arxiv.org/pdf/1711.11224

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关键词：Segmentation Architecture Mathematical Applications Presentation Convolution 空间 方法 linear dimensional