Neural network decision directed edge-adaptive Kalman filter for image estimation

Abstract

Abstract-A neural network-based scheme for decision directed edgeadaptive Kalman filtering is introduced in this work. A backpropagation neural network makes the decisions about the orientation of the edges based on the information in a window centered at the current pixel being processed. Then based upon the neural network output an appropriate image model which closely matches the local statistics of the image is chosen for the Kalman filter. This prevents the oversmoothing of the edges, which would have otherwise been caused by the standard Kalman filter. Simulation results are presented which show the effectiveness of the proposed scheme.

Real‐time state estimator without noise covariance matrices knowledge – fast minimum norm filtering algorithm

“…Comparing with other issues, issue (c) may be relatively easy to resolve, and one typical approach has been mentioned above if we have some physical or a priori knowledge on the sources of possible errors in the sensors. As to issue (d), there exists one approach called AKF [22,26,27], whose idea is to adaptively estimate the uncertain statistical properties of the noises and combine the Kalman filter with the modified covariance matrices. Kalman filter based on support vector machine [28] may be regarded as another example to deal with the issue (d).…”

On the correlation structure of unilateral AR processes on the plane

“…Still, there remains constant interest in 2-D AR models in those applications where low complexity is required and may be achieved by recursivity. Recent developments include image enhancement through adaptive recursive and/or lattice filtering [1,14] and image predictive compression [23,24]. In parallel, the theoretical field has addressed some unresolved issues related either to 2-D AR models themselves [27] or to the closely connected problem of stability tests for 2-D recursive linear filters [16,18].…”

“…QPARs (and UARs, more generally) are usually considered as the most straightforward generalization of 1-D AR processes to the Z 2 plane, but very little is known about their correlation structure. Closed-form expressions for the correlations are available in the case of QPARs of order (1,1) only [2,27]. In the general QPAR case, the Yule-Walker equations only yield recursive formulas for the correlations in the positive quadrant, without the appropriate boundary conditions.…”

“…In the general QPAR case, the Yule-Walker equations only yield recursive formulas for the correlations in the positive quadrant, without the appropriate boundary conditions. Therefore, computation of the correlations eventually resorts to numerical inversion of the power spectral density (PSD), as in the case of any wide-sense stationary MRF on Z 2 . Whereas no such equivalence theorem is explicitly asserted by Tory and Pickard [27], it can be inferred from their work that the class of QPARs of order (1,1) identifies with the class of Gaussian Pickard random fields (PRFs) on Z 2 [25]. PRFs exhibit some very unusual properties.…”

“…Moreover, these features enable exact computation of the likelihood on any finite rectangular lattice under the Gaussian assumption. The equivalence between QPARs of order (1,1) and Gaussian PRFs underlies another unusual property: the restriction of a QPAR(1, 1) on a finite rectangular lattice preserves a small neighborhood structure at the boundaries of the lattice. The resulting distribution is a particular case of a 'stationary MRF on a finite rectangular lattice', as defined in [5].…”