Fast Approximations of Shift-Variant Blur
Fast Approximations of Shift-Variant Blur
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DOI：
10.1007/s11263-015-0817-x
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发表时间：
2015-12-01
影响因子：
19.5
通讯作者：
Mourya, Rahul
中科院分区：
文献类型：
--
作者：
Denis, Loic;Thiebaut, Eric;Mourya, Rahul
图像去模糊对于高分辨率成像至关重要，例如天文学、显微镜或计算摄影。平移不变模糊完全由单点扩散函数 (PSF) 表征。然后通过卷积对模糊进行建模，从而产生依赖于快速傅里叶变换的有效模糊模拟和消除算法。然而，在许多不同的情况下，模糊不能被认为是在整个视场中恒定的，因此需要对 PSF 随位置的变化进行建模。这些模型必须在其灵活性所能达到的精度和计算效率之间实现权衡。文献中已经提出了几种快速的模糊近似方法。我们根据模糊算子的矩阵分解对这些方法进行了统一的表述。我们建立了文献中可以找到的不同计算技巧与等效 PSF 方面相应近似值的物理意义之间的联系，基于物理的近似值更好。我们推导出一种改进的近似，它保留了与其他快速算法相同的理想的低复杂性，同时达到了最小的近似误差。每种模糊近似的理论特性和经验性能的比较表明，所提出的通用模型更适合已知移变模糊的近似和反演。
Image deblurring is essential in high resolution imaging, e.g., astronomy, microscopy or computational photography. Shift-invariant blur is fully characterized by a single point-spread-function (PSF). Blurring is then modeled by a convolution, leading to efficient algorithms for blur simulation and removal that rely on fast Fourier transforms. However, in many different contexts, blur cannot be considered constant throughout the field-of-view, and thus necessitates to model variations of the PSF with the location. These models must achieve a trade-off between the accuracy that can be reached with their flexibility, and their computational efficiency. Several fast approximations of blur have been proposed in the literature. We give a unified presentation of these methods in the light of matrix decompositions of the blurring operator. We establish the connection between different computational tricks that can be found in the literature and the physical sense of corresponding approximations in terms of equivalent PSFs, physically-based approximations being preferable. We derive an improved approximation that preserves the same desirable low complexity as other fast algorithms while reaching a minimal approximation error. Comparison of theoretical properties and empirical performances of each blur approximation suggests that the proposed general model is preferable for approximation and inversion of a known shift-variant blur.