Lattice algorithms applied to the blind deconvolution problem

The blind deconvolution problem is to reconstruct a sequence {r_k} from noisy observations y_k= S_k×r_k+n_k where {r_k} and {S_k} are both unknown. It is assumed that {S_k} is deterministic and minimum phase, {r_k} is a realization of a white process, and {n_k} is white Gaussian noise. The novelty of the approach is the use of lattice-based algorithms for all parts of the problem. First, the Burg method is used to estimate the magnitude of S_s(f)=F {s_k}. Second, the Schur algorithm is used to compute the spectral factor of |S_s(f)|, yielding {s_k}. Finally, the Levinson algorithm is used to solve the Toeplitz equations for the estimate of {r_k}. Results of numerical simulations are presented