NONNEGATIVITY CONSTRAINED SPECTRAL FACTORIZATION FOR IMAGE RECONSTRUCTION FROM AUTOCORRELATION DATA.

The authors consider the factorization of the 1-D and 2-D spectral density functions (z-transforms of real-valued autocorrelation sequences), S(z) and S(z//1,z//2) in the forms Sz equals F(z)F(z**-**1) and S(z//1, z//2) equals F(z//1, z//2) F(z//1**-**1, z//2**-**1), respectively where the coefficient of polynomials F(z) and F(z//1, z//2) are constrained to be nonnegative. The problem is solved only in special cases. In the general situation, the scopes for adapting and generalizing the iterative techniques available for the classical 1-D spectral factorization problem to tackle the nonnegativity constrained spectral factorization problem under study have been analyzed.