Super-resolution Restoration of Continuous Image Sequence - Adaptive Filtering Approach

In this paper, we propose computationally efficient super-resolution restoration algorithms for blurred, noisy and down-sampled continuous image sequences. The proposed approach is a generalization of the stochastic estimation based methods (the ML and the MAP estimators) for the restoration of single blurred and noisy images. The blur, decimation, and noise degredations are modeled as a sparse matrices linear equation connecting the measurements to the ideal required image. A second linear equation can be added in order to include a localy adaptive spatial smoothness prior, similar to the way it is done in the Constrained Least Squares method. Based on these two equations, a classic super-resolution restoration approach can be suggested as a by-product of the above formulation. This way, a single improved resolution image can be restored from several warped, blurred, noisy and down-sampled versions of it. The adaptive spatial regularization term is shown to improve the restored image sequence quality by forcing smoothness, while preserving edges. When attempting to treat continuous image sequences, the temporal axis is to included into the model. This is done by using temporal smoothness assumption along motion trajectories, resulting with a calssic state-space equations model. The obtained model can serve as a basis for the application of the Kalman filter (KF), but a direct application of the KF is far to complex to imlement. The state-space equations model are thus further simplified, yielding a Least Squares (LS) model an instantaneous squared error quality measure which is to be minimized over time. The RLS and LMS adaptive algorithms can be applied directly to the new simplified model. This way, simple yet very effective two recursive algorithms for the estimation of the restored improved resolution image sequence in time are composed. The computation complexity of the obtained algorithms is of the order O L L { log } 2 ( ) per one output image, where L2 is the number of pixels in the output image. Simulations carried out on test sequences prove these methods to be applicable, efficient, and with very promising results.