A novel random singular value decomposition based on optica

• 1、 School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, 100876, China
• 2、 State Key Laboratory of Information Photonics and Optical Communications, Beijing, 100876, China

Abstract：Random singular value decomposition (RSVD) is an improvement of singular value decomposition (SVD) algorithm. RSVD is widely used in data compression, signal processing and image noise reduction. However, the increasing matrix scale puts forward higher requirements for the hardware platform.In order to achieve RSVD of large-scale matrices, this paper presents a scheme of RSVD based on space optical computing platform.The initial matrix information is loaded onto the optical signal through the spatial light modulator, and the dimension of the matrix is reduced by using the random projection property of the optical complex medium. Finally, the reduced dimension matrix is decomposed by singular value decomposition.This scheme no longer needs to generate and store random Gaussian matrix, which solves the bottleneck problem restricting the application of rsvd. The experimental results show that the accuracy of radom singular value decomposition is affected by the quantization accuracy of matrix elements, matrix dimension reduction sampling rate, scattering medium.At 1550nm wavelength, 0.5sample ratio, and the mcopixel is 100×100, the relative error of RSVD can be less than 0.1 when ground-glass is used as a complex medium.In addition, this paper uses this scheme to complete the task of image compression, which provides a new idea for the further study of large-scale image matrix processing algorithm.

Keywords： random singular value decomposition optical computing optical complex medium matrix dimensionality reduction image compression