Stochastic modelling and 3D minimum variance recursive estimation of image sequences
The main goals of the paper are (1) to investigate the noisy image sequence restoration problem, and (2) to propose a causal, 3D, minimum variance, recursive filter with edge-preserving properties. The proposed spatio-temporal filter is derived according to the assumption that the 3D signal can be modelled by an ensemble of smooth 3D Gaussian random fields. In the filtering algorithm, on each frame of the image sequence, the 3D filtered estimate is obtained as the combination of three 1D estimates whose optimality is proved. This algorithm property is a consequence of the state-space representation of the image sequence, which is composed of three 1D dynamic state equations with independent white noise inputs, and follows from the basic smoothness, stochastic, and inhomogeneity assumptions. Another important feature of the filter is that it does not require motion estimation, image non-stationarities being taken into account by the spatio-temporal variant structure of the filter. Structural information on 3D edge location is included in the signal model, being obtained by means of a 3D noise smoothing difference operator. Numerical results demonstrate good performance both in terms of Signal-to-Noise-Ratio Improvement (SNRI) and of visual quality of restored images. Satisfactory results are also obtained for low values of SNR, which usually provide a critical behaviour of motion compensated filters.
scientific article; zbMATH DE number 1359933