Binary filter estimation for large windows

Optimal filters are characterized by parameters based on image and filter structure and these parameters need to be estimated from realizations. For fully optimal mean-absolute-error binary filters, conditional expectations need to be estimated. Owing to lack of estimation precision, the resulting estimated filter is likely to be suboptimal. The estimation dilemma can be mitigated by using a constrained filter requiring less parameters. This paper examines the relationship between estimation precision and constraint. It focuses on binary filters, relevant Chebyshev bounds, and the relationships between the kernels of optimal, constrained, and estimated filters. It describes constraint via iterative design and secondarily constrained filters, as well as using suboptimal filters as prior filters for the estimation of optimal filters using new data.