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摘要翻译：
讨论了在给定精度下，数字图像采集和重建所需的测量次数最小化的问题。本文概述了采样理论的基本原理，指出在给定精度下，信号采样率的下界等于具有该精度的信号稀疏近似的频谱稀疏性。结果表明，作为解决采样率最小化问题而提出的压缩感知方法远未达到理论上的采样率最小值。通过一个简单直观的模型，揭示了压缩感知的潜力和局限性，提出了一种图像任意采样和有界谱重构方法（ASBSR-method）,该方法可以逼近图像采样率的理论最小值。本文还讨论了ASBSR方法的实验验证结果及其在解决各种欠定逆问题中的可能适用性扩展，如彩色图像去马赛克、图像内绘制、由稀疏采样或抽取投影重建图像、由其傅立叶谱模重建图像以及由其稀疏采样在傅立叶域重建图像等
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英文标题：
《Compressed Sensing, ASBSR-method of image sampling and reconstruction
and the problem of digital image acquisition with the lowest possible
sampling rate》
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作者：
Leonid P. Yaroslavsky
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最新提交年份：
2018
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分类信息：
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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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：
The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling rate sufficient for signal reconstruction with a given accuracy is equal to the spectrum sparsity of the signal sparse approximation that has this accuracy. It is revealed that the compressed sensing approach, which was advanced as a solution to the sampling rate minimization problem, is far from reaching the sampling rate theoretical minimum. Potentials and limitations of compressed sensing are demystified using a simple and intutive model, A method of image Arbitrary Sampling and Bounded Spectrum Reconstruction (ASBSR-method) is described that allows to draw near the image sampling rate theoretical minimum. Presented and discussed are also results of experimental verification of the ASBSR-method and its possible applicability extensions to solving various underdetermined inverse problems such as color image demosaicing, image in-painting, image reconstruction from their sparsely sampled or decimated projections, image reconstruction from the modulus of its Fourier spectrum, and image reconstruction from its sparse samples in Fourier domain
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PDF链接：
https://arxiv.org/pdf/1710.05985
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