Greedy sparse spectral factorization using reduced-size Gram matrix parameterization

In this paper we deal with retrieving the spectral factor for an autocorrelation polynomial with only a few nonzero elements. The algorithm is based on the representation of polynomials using sparse bases. We search in a greedy way for a basis by removing elements from the basis of the autocorrelation polynomial and extracting the spectral factor, using a semidefinite program. The algorithm stops when no other solution can be obtained with a smaller basis. Our algorithm appears to be faster and can be more accurate than previous methods.