A robust Kalman filter design for image restoration

Abstract

In image deconvolution or restoration using a Kalman filter, the image and blur models are required to be known for the restoration process. Generally, the accuracy of the restoration depends on the accuracy of the given models. Unfortunately, the image and blur models are normally unknown in practice. To solve the problem, an identification stage is employed to estimate the image and blur models. However, the estimated models are seldom accurate, especially with the presence of noise in the image. This paper presents a robust Kalman filter design for image deconvolution that can accommodate the inaccuracy in the estimated image and blur models. If the inaccuracy can be modelled as additive white Gaussian noise with a known variance, it can be stochastically accounted for in the robust filter design. In the simulation tests performed, the robust design achieved improved accuracy in the image restoration, even though inaccurate image and blur models were used.