基于光子计算的随机奇异值分解

Randomized Singular Value Decomposition Based on Optical Computation

随机奇异值分解(RSVD)在数据压缩、信号处理和图像降噪等方面具有广泛的应用,但日益剧增的矩阵规模对传统计算平台提出了更高的内存需求。为此,提出了基于空间光计算的RSVD方法。利用复杂介质的固有性质将矩阵降维,不再需要生成和存储随机高斯矩阵,能够有效降低RSVD的计算开销。实验证明,在采样率为0.2、宏像素块维度为10×10、选用220目毛玻璃作为散射介质的情况下,所提方法能够对维度为80×80的矩阵实现RSVD,其相对误差小于0.1,与传统方法相比,有效降低了RSVD的时间复杂度和空间复杂度。最后,通过图像压缩验证了所提方法的效果,所提方法为进一步研究大规模图像矩阵算法提供了基础。

As randomized singular value decomposition(RSVD)is widely used in data compression,signal processing and image denoising,the increasing matrix scale puts forward higher requirements for the traditional computing platform.Therefore,a scheme of RSVD based on the spatial optical computation is proposed.The dimensions of a matrix are reduced by the inherent properties of the complex media,and there is no need to generate and store random Gaussian matrices.In this way,the computing overhead of RSVD can be effectively reduced.The experiment proves that the proposed scheme can achieve RSVD for a 80×80 matrix with a relative error of less than 0.1 when 220 mesh ground glass is used as a complex medium,the sampling rate is 0.2,and the dimension of macropixel block is 10×10.Compared with the traditional method,it effectively reduces the time complexity and space complexity of RSVD.Finally,the effect of the scheme is verified through image compression,which provides a basis for further research on large-scale image matrix algorithms.