How to program the fitness function of PSO on SVD denoising

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luo yisheng 2015-6-12

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https://ww2.mathworks.cn/matlabcentral/answers/223538-how-to-program-the-fitness-function-of-pso-on-svd-denoising

回答： GEETHANJALI K 2018-3-13

I want to use the PSO algorithm to optimize the SVD noise reduction,utilize the SNR of de-noised signal for the fitness function of PSO.Provided there are a pure signal s(t)=[s1(t),s2(t),...,sN(t)]' and a noise signal x(t)=[x1(t),x2(t),...,xN(t)]'.Constructing a Hankel matrix X of m×n dimension on the noise signal x(t),then applying SVD on the Hankel matrix X=USV',where matrix U is m×m dimension,matrix S is m×n dimension,and matrix V is n×n dimension.According to the maximum of singular value difference to determine the reconstruction order rank k of singular values.Pice up the first k column of matrix U and V,the first k row and first k column of matrix S,then obtain the sub-matrix u of m×k dimension,s of k×k dimension and v of n×k dimension.Supposed there is a diagonal matrix A of k×k dimension.The estimated matrix of pure signal is E_X=uAsv',so the estimated pure signal is ss=[E_X(1,:) E_X(2:end,end)'],and the SNR=10*log10(s(t)^2)/((s(t)-ss(t))^2). Above all,I want to know how to program the fitness function of PSO?Thank you!