Research On Optical Implementation Of Matrix Multiplication

Many problems of scientific computing can usually be transformed into matrix operations in the field of modern science.Matrix multiplication is a basic matrix operation,which is widely used in linear equations solving,engineering control and image processing.Optical information processing technology has the advantages of parallelism,ultra high speed,large capacity and spatial interconnection,and the rapid processing for large amount of data can be realized by it.Optical matrix multiplication is implemented utilizing optical information processing technology,which improve the computing efficiency effectively.Therefore,an optical implementation method of matrix-matrix multiplication is proposed,which is described as follows:1.By analyzing the matrix multiplication theory and the principle of the optical 4f system,a matrix multiplication method based on the convolution operation is proposed.2.The mathematical model of the relationship between matrix multiplication and optical filter is established.The coding method of optical matrix multiplication filter and the corresponding decoding method are proposed.According to the special requirement of the image loading device and the image acquisition device in the real optical 4f system,the space filter is separated by positive and negative,and the frequency domain filter is normalized and quantized.Then the non-negative optical matrix multiplication filter is obtained.In addition,considering the influence of image spatial frequency characteristics,the limitation of spatial filtering range and system noise in 4f system,the physical size of the input image and the optical filter are designed.3.The matrix multiplication is implemented utilizing optical 4f system.The input matrix image and the filter are placed on the input plane and spectrum plane of the system respectively utilizing the amplitude SLM.The CCD is placed on the output plane to collect the optical matrix convolution results.Finally,the optical matrix multiplication result is obtained by the corresponding decoding.4.It is necessary to perform threshold segmentation and quantization before decoding the optical experiment results collected by CCD for the accuracy of the experimental results.Then the post-processing operations,i.e.inverse normalization,subtraction of positive and negative components are performed.The numerical simulation experiments are carried out utilizing MATLAB software on the condition of the quantization error or not.The actual optical 4f system is constructed to carry out the optical matrix multiplication experiment.On the ideal condition,the simulation results are agree with the theoretical values,and the simulation results on the condition of quantization error have little errors compared with the theoretical values.The optical experiments have also better accuracy.The experiment results verified the proposed method.