Recursive Kalman type filter selection for adaptive image restoration

Abstract

Summary form only given. The one-dimensional state-space representation of an image for restoration using a Kalman filter requires a relatively large state vector. For typical autoregressive moving-average (ARMA) signal models with nonsymmetric half-plane support, the dimension of the state is approximately equal to the product of the image model order and the pixel width of the image. This state is quite large, particularly for practical images, and would require excessive computation if the Kalman filter were used directly for adaptive restoration (in response to identified parameter changes). To overcome these limitations, three approximations to the Kalman filter have been offered for adaptive restoration: the reduced-update Kalman filter (RUKF), the reduced-order-model Kalman filter (ROMKF), and the Chandrasekhar filter. The authors have compared the performances of the three techniques, based on a model identified by another program, and have investigated the feasibility of applying the Chandrasekhar algorithm to continuous adaptive restoration (i.e. with nonstationary parameters). They have shown that the filter gains computed by the approximate RUKF and ROMKF procedures are nearly optimal and that the fast but true optimal Chandrasekhar filter is not suitable for adaptive processes. >