90Chapter 15.Solutions: Case Study: Blind Deconvolution: A Matter of Norm∂F(e,f)∂f ∂fq=mi=1(ki+ei)(kiq+eiq) = ((K+E)T(K+E))q,where out-of-range entries in summations are assumed to be zero andRis a matrixwhose nonzero entries are components ofr. Sog=∇F(e,f) =D2e−FTr(K+E)Tr,H(e,f) =D2+FTFRT+FT(K+E)R+ (K+E)TF(K+E)T(K+E).The Newton direction is the solution toH(e,f)p=−g.CHALLENGE 15.3.The least squares problem is of the formminxAx−b2,wherex=ΔeΔfandAandbare the given matrix and vector. So to minimizeAx−b2= (Ax−b)T(Ax−b), we set the derivative equal to zero, obtainingATAx−ATb=0.The solution to this equation is a minimizer if the second derivative
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