去模糊离散高斯模糊

B. Mair, D.C. Wilson, Z. Réti
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引用次数: 5

摘要

1995年,Z. Reti提出了一种消除离散高斯模糊图像的方法。该方法是基于从高斯、G.雅可比(1829)和拉马努金发展的解析数论中借用的定理。该方法相对于连续域的同类方法的一个优点是它提供了去模糊卷积的精确公式。此外,在连续域高斯模型的去模糊是一个不适定逆问题,而对离散高斯模型的去模糊则是一个数学上的适定问题。这里给出的公式提供了将重建图像的质量与模糊图像的质量联系起来的误差界限。这种去模糊方法被方便地表示为Toeplitz矩阵的乘法,该矩阵的对角线项呈指数减少,从而使该方法适合于数值近似。条件数提供了各种选择/spl σ /。
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Deblurring the discrete Gaussian blur
In 1995 Z. Reti presented a method for deblurring images blurred by the discrete Gaussian. The method is based on theorems borrowed from analytic number theory developed by Gauss, G. Jacobi (1829), and Ramanujan. One advantage of this method over similar ones developed for the continuous domain is that it provides exact formulas for the deblurring convolution. In addition, while deblurring the Gaussian in the continuous domain is an ill-posed inverse problem, deblurring the discrete Gaussian model results in a mathematically well-posed problem. The formulas presented here provide error bounds which relate the quality of the reconstructed image to that of the blurred image. This deblurring method is conveniently expressed in terms of multiplication by Toeplitz matrices whose diagonal entries decrease exponentially, thus rendering the method suitable for numerical approximations. Condition numbers are provided for various choices of /spl sigma/.
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