RESOLUTION IN DIFFRACTION-LIMITED IMAGING, A SINGULAR VALUE ANALYSIS .3. THE EFFECT OF SAMPLING AND TRUNCATION OF THE DATA
RESOLUTION IN DIFFRACTION-LIMITED IMAGING, A SINGULAR VALUE ANALYSIS .3. THE EFFECT OF SAMPLING AND TRUNCATION OF THE DATA
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DOI：
10.1080/713821480
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发表时间：
1984-01-01
期刊：
影响因子：
--
通讯作者：
PIKE, ER
中科院分区：
文献类型：
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作者：
BERTERO, M;BRIANZI, P;PIKE, ER
在之前的两篇论文中，我们考虑了衍射限制成像问题中的物体恢复问题，其中允许物体和图像域不同。的调查进行的奇异函数和奇异值，而不是通常的特征函数和特征值，适用于几何成像。我们推导了图像的自由度，并得到了新的分辨率限制。更实际地，在实际衍射实验中，图像数据仅在一组采样点处已知，而不是作为连续函数。奇异值分析的力量是这样的，但是，我们可以修改以前的工作，考虑连续目标函数到向量数据函数的映射作为一个奇异系统。本文进行了这方面的工作，找到了适合于采样图像和连续对象的新的奇异值、奇异函数和奇异向量，证明了当图像点的个数趋于无穷大时，离散问题的奇异系统收敛到连续问题的奇异系统。
In two previous papers we have considered the problem of object restoration in diffraction-limited imaging problems where the object and image domains are allowed to differ. The investigations were performed in terms of singular functions and singular values, instead of the usual eigenfunctions and eigenvalues which apply to geometrical imaging only. We deduced the number of degrees of freedom of the image and obtained new resolution limits. More realistically, in an actual diffraction experiment the image data are known only at a set of sampled points rather than as a continuous function. The power of the singular value analysis is such, however, that we may modify the previous work to consider the mapping of continuous object functions into vector data functions as a singular system. This is carried out in the present paper, and new singular values, functions and vectors appropriate to a sampled image and continuous object are found. We prove that when the number of image points tends to infinity, the singular system of the discrete problem converges to the singular system of the continuous problem.