Two-dimensional adaptive block Kalman filtering of SAR imagery

Abstract-A new neural network-based approach is introduced for recursive computation of the principal components of a stationary vector stochastic process. The neurons of a single layer network are sequentially trained using a recursive least squares squares (RLS) type algorithm to extract the principal components of the input process. The optimality criterion is based on retaining the maximum information contained in the input sequence so as to be able to reconstruct the network inputs from the corresponding outputs with minimum mean squared error. The proof of the convergence of the weight vectors to the principal eigenvectors is also established. A simulation example is given to show the accuracy and speed advantages of this algorithm in comparison with the existing methods. Finally, the application of this learning algorithm to image data reduction and filtering of images degraded by additive and/or multiplicative noise is considered.

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“…then, the optimal weight vector w m (n) that minimizes the error function Jm(n) can be obtained, in a manner similar to (17), as…”

Section: ) Extracting the First Principal Componentmentioning

confidence: 99%

“…The recorded image in presence of both multiplicative speckle noise and additive thermal noise can be modeled as [17] (43) procedures on the Boat image of Fig. 12.…”

Section: Image Filteringmentioning

confidence: 99%

Principal component extraction using recursive least squares learning

Bannour

Azimi-Sadjadi

1995

IEEE Trans. Neural Netw.

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116

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“…(5b) Transposing (5a) and using the property (6) which is the normal equation for this estimator. Plugging I = 0, 1 in this equation gives the following vector YuleWalker equation…”

Section: Pij(!)~e[xi(n)\j(n -I)]mentioning

confidence: 99%

“…This, obviously, leads to an excessively large amount of storage and computations. A number of researchers introduced various filtering schemes [3]- [6] to overcome these problems. The idea of the reduced update Kalman filtering (RUKF) [4]- [6] is to partition the state vector into two segments-the "local state" and the "global state."…”

Section: Introductionmentioning

confidence: 99%

“…A number of researchers introduced various filtering schemes [3]- [6] to overcome these problems. The idea of the reduced update Kalman filtering (RUKF) [4]- [6] is to partition the state vector into two segments-the "local state" and the "global state." The "local state" propagates in both dimensions during the filtering process and consists of a group of pixels, in the region of support (ROS) of the model, which are spatially close to the points being estimated.…”

Section: Introductionmentioning

confidence: 99%

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A full-plane block Kalman filter for image restoration

Citrin

Azimi-Sadjadi

1992

IEEE Trans. on Image Process.

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Abstract-A new two-dimensional (2-D) block Kalman filtering method is presented which uses a full-plane image model to generate a more accurate filtered estimate of an image that has been corrupted by additive noise and full-plane blur. Causality is maintained within the filtering process by employing multiple concurrent block estimators. In addition, true state dynamics are preserved, resulting in an accurate Kalman gain matrix. Simulation results on a test image corupted by additive white Gaussian noise are presented for various image models and compared to those of the previous block Kalman filtering methods.

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Weighted fusion robust steady‐state estimators for multisensor networked systems with one‐step random delay and inconsecutive packet dropouts

Liu

Deng

2019

Adaptive Control & Signal

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Summary In this paper, the weighted fusion robust steady‐state Kalman filtering problem is studied for a class of multisensor networked systems with mixed uncertainties. The uncertainties include same multiplicative noises in system parameter matrices, uncertain noise variances, as well as the one‐step random delay and inconsecutive packet dropouts, which modeled by sequences of Bernoulli variables with different probabilities. By defining a new observation vector and applying the augmented method, the system under study is converted into one with only uncertain noise variances. The sufficient conditions for the existence of steady‐state estimators are given. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are proposed. Applying the optimal fusion algorithm weighted by matrices and the covariance intersection fusion algorithm, the two kinds of robust fusion steady‐state Kalman estimators are derived in a unified framework. The robustness of the proposed fusion estimators is proved by applying the permutation matrices and the global Lyapunov equations method, such that, for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fusion steady‐state Kalman estimators are proved. An example with application to autoregressive moving average signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.

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Two-dimensional adaptive block Kalman filtering of SAR imagery

Cited by 38 publications

References 28 publications

Principal component extraction using recursive least squares learning

Principal component extraction using recursive least squares learning

A full-plane block Kalman filter for image restoration

Weighted fusion robust steady‐state estimators for multisensor networked systems with one‐step random delay and inconsecutive packet dropouts

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