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2. 发明申请

US20120221617A1 Methods and apparatus for fast matrix multiplication and fast solving of matrix equations based on generalized convolution 审中-公开
标题翻译：基于广义卷积的快速矩阵乘法和矩阵方程快速求解的方法和装置
公开(公告)号：US20120221617A1
公开(公告)日：2012-08-30
申请号：US13136566
申请日：2011-08-04
申请人： Muralidhara Subbarao , Shekhar Bangalore Sastry , Satyaki Dutta
发明人： Muralidhara Subbarao , Shekhar Bangalore Sastry , Satyaki Dutta
IPC分类号： G06F17/11 , G06F17/14 , G06F17/16 , G06F1/02
CPC分类号： G06F17/16 , G06F17/13
摘要： A method of fast matrix multiplication and a method and apparatus for fast solving of a matrix equation are disclosed. They are useful in many applications including image blurring, deblurring, and 3D image reconstruction, in 3D microscopy and computer vision. The methods and apparatus are based on a new theoretical result—the Generalized Convolution Theorem (GCT). Based on GCT, matrix equations that represent certain linear integral equations are first transformed to equivalent convolution integral equations through change of variables. Then the resulting convolution integral equations are evaluated or solved using the Fast Fourier Transform (FFT). Evaluating a convolution integral corresponds to matrix multiplication and solving a convolution integral equation corresponds to solving the related matrix equation through deconvolution. Carrying-out these convolution and deconvolution operations in the Fourier domain using FFT speeds up computations significantly. These results are applicable to both one-dimensional and multi-dimensional integral equations.
摘要翻译：公开了一种快速矩阵乘法的方法和用于快速求解矩阵方程的方法和装置。它们在许多应用中是有用的，包括3D显微镜和计算机视觉中的图像模糊，去模糊和3D图像重建。方法和装置基于新的理论结果 - 广义卷积定理（GCT）。基于GCT，表示某些线性积分方程的矩阵方程首先通过变量变换转换为等效卷积积分方程。然后使用快速傅立叶变换（FFT）来评估或求解所得到的卷积积分方程。评估卷积积分对应于矩阵乘法，并求解卷积积分方程对应于通过去卷积求解相关矩阵方程。使用FFT在傅立叶域中进行这些卷积和去卷积运算，显着加快了计算。这些结果适用于一维和多维积分方程。

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