2-D blind deconvolution using Fourier series-based model and higher-order statistics with application to texture synthesis

With a given set of non-Gaussian output measurements of a 2D linear shift-invariant (LSI) system, a 2D blind deconvolution algorithm is proposed that uses Chi's Fourier series-based model (FSBM) for the unknown system and the cumulant-based inverse filter criteria proposed by Chi (1994) and Wu, and Tuganit (1994). The proposed algorithm is an iterative optimization algorithm that is computationally efficient with a parallel structure. The estimated FSBM for the unknown system that can be nonseparable or noncausal, is guaranteed to be stable. The application of the proposed algorithm to texture synthesis with real texture images is also presented, in addition to some simulation results. Finally, we draw some conclusions.