On state-space signal processing with application to image enhancement

INTEODUCTION Recently there has been much interest in the use in digital signal processing [11. Since the state variables ae used, this class of techniques will be called state—space signal processing in this paper. In particular the paper is concerned with the application of Kalman filtering and related recursive estimation techniques for image enhancement. There has been nuch work on this Without the object boundaries, an image nay be modelled as a honogeneous random field. Wiener filtering, Kaiman filtering, and nany other procedures nay be used to snooth the image. Kalman filtering has the advantages over the others in that it is suitable for real-tine operation, requiring little parametric information of the image model, and that it can adapt to the textural and temporal variations in the image. In practice the cbject boundaries should be considered in image enhancement and the image should be mcdelled as a shift—variant system rather than a shift—invariant system. Kalman filtering is particularly suitable for such an image model. Recently an adaptive filtering method has been proposed for detection and estimation of the jumps by using the Kalman filter and a generalized likelihood ratio technique [6]. The basic idea is that Kalman filter is implemented on the assumption that there is no state jumps, and a second system is designed to monitor the measurement residuals of the filter to determine if a change has occurred and adjust the filter accordingly. When the transition matrix of the Kalmam filter is unknown, it can be determined by a method of simultaneous estimation of parameters and states [7]. The combination of the work in Ref s. 6 & 7 is adpated to image enhancement with reconnaissance imagery. The resulting improvement even under very small signal— to—noise ratio is very significant. Detailed mathematical formulation and computer results are presented in the following sections. It should be emphasized that the mathematical techniques presented are very useful to all state—space signal processing problems.