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(z₁, z₂) in the forms Sz=F(z)F(z^-1) and S(z₁, z₂)=F(z₁, z ₂) F(z₁^-1, z ₂^-1), respectively where the coefficient of polynomials F(z) and F(z₁, z₂) 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