NEW FAST RECURSIVE ALGORITHMS FOR SIMULTANEOUS RECONSTRUCTION AND IDENTIFICATION OF AR PROCESSES WITH MISSING OBSERVATIONS

This paper deals with the problem of adaptive reconstruction and identification of AR processes with randomly missing observations. The performances of a previously proposed real time algorithm are studied. Two new alternatives, based on other predictors, are proposed. They offer an unbiased estimation of the AR parameters. The first algorithm, based on the h-step predictor, is very simple but suffers from a large reconstruction error. The second one, based on the incomplete past predictor, offers an optimal reconstruction error in the least mean square sense

Identifcation stable et reconstruction robuste de signaux non stationnaires à échantillons manquants

National audienceOn souhaite reconstruire en ligne un signal à échantillons manquants. Lorsque la perte est élevée les méthodes existantes peuvent conduire à l'identifcation de modèles instables. Nous proposons, à notre connaissance, le premier algorithme qui permet le traitement en ligne des signaux à échantillons manquants utilisant la structure en treillis du filtre. La robustesse à un fort taux de perte et la stabilité du modèle ainsi identifié sont garanties. Les performances de ce nouvel algorithme dépassent celles des algorithmes existants et ce d'autant plus que la probabilité de perte est forte

NEW FAST ALGORITHM FOR SIMULTANEOUS IDENTIFICATION AND OPTIMAL RECONSTRUCTION OF NON STATIONARY AR PROCESSES WITH MISSING OBSERVATIONS

International audienceThis paper deals with the problem of adaptive reconstruction and identification of AR processes with randomlymissing observations. A new real time algorithm is proposed. It uses combined pseudo-linear RLS algorithm and Kalman filter. It offers an unbiased estimation of the AR parameters and an optimal reconstruction error in the least mean square sense. In addition, thanks to the pseudo-linear RLS identification, this algorithm can be used for the identification of non stationary AR signals. Moreover, simplifications of the algorithm reduces the calculation time, thus this algorithm can be used in real time applications

Adaptive transmission for lossless image reconstruction

International audienceThis paper deals with the problem of adaptive digital transmission systems for lossless reconstruction. A new system, based on the principle of non-uniform transmission, is proposed. It uses a recently proposed algorithm for adaptive stable identification and robust reconstruction of AR processes subject to missing data. This algorithm offers at the same time an unbiased estimation of the model's parameters and an optimal reconstruction in the least mean square sense. It is an extension of the RLSL algorithm to the case of missing observations combined with a Kalman filter for the prediction. This algorithm has been extended to 2D signals. The proposed method has been applied for lossless image compression. It has shown an improvement in bit rate transmission compared to the JPEG2000 standard

Algorithmes adaptatifs d'identification et de reconstruction de processus AR à échantillons manquants

We are concerned in online reconstruction of signals subject to missing samples using a parametric approach. We propose adaptive algorithms for identification and reconstruction of AR processes with missing samples. Firstly, we consider the extension of gradient algorithms to the case of signals with missing samples. We propose two alternatives to an existent algorithm based on two other predictors. The proposed algorithms converge toward unbiased estimation of the parameters. However, gradient algorithms suffer from slow convergence. Therefore, we consider the RLS algorithm extension to the case of signals subject to missing samples. We use jointly, the pseudo-linear RLS algorithm for the identification and a Kalman filter for optimal reconstruction of the signal in the least mean square sense. The estimated parameters, using the proposed algorithm, are unbiased. In addition, it is fast and well adapted to the identification of non stationary signals. Nevertheless, looking for the control of the identified filter stability, we propose to identify the signal using the lattice structure of the filter. We propose an extension of the Burg adaptive algorithm to the case of signals subject to missing observations, using a Kalman filter for the prediction. The estimated parameters guarantee the stability of the corresponding filter. In addition, it offers a faster tracking parameter. Finally, we use the proposed algorithms in non uniform transmission systems. We then get the improvement of both the SNR and the average transmission rate.On souhaite reconstruire en ligne des signaux à échantillons manquants en utilisant une approche paramétrique. On propose alors des algorithmes adaptatifs d'identification et de reconstruction de processus AR à échantillons manquants. On s'intéresse premièrement à l'extension des algorithmes de gradient au cas des signaux à échantillons manquants. On propose alors deux alternatives à un algorithme existant fondées sur deux autres prédicteurs. Les algorithmes proposés convergent vers une estimation non biaisée des paramètres. Or les algorithmes de gradient souffrent d'une faible vitesse de convergence. Pour cela, on s'intéresse à l'extension de l'algorithme MCR au cas des signaux à échantillons manquants. On utilise alors l'algorithme MCR pseudo-linéaire pour l'identification conjointement avec un filtre de Kalman pour une prédiction optimale du signal au sens des moindres carrés. L'algorithme résultant permet une identification non biaisée des paramètres. De plus, il est rapide et bien adapté à l'identification de processus non stationnaires. Néanmoins, souhaitant contrôler la stabilité du filtre identifié, on s'intéresse ensuite à une identification fondée sur une structure en treillis du filtre. Ainsi, on propose une extension de l'algorithme de Burg adaptatif au cas des signaux à échantillons manquants, en utilisant pour la prédiction un filtre de Kalman. La stabilité du modèle ainsi identifié est garantie. De plus, l'algorithme s'adapte rapidement aux variations des paramètres. Finalement, on propose d'utiliser les algorithmes proposés dans un système à transmission non uniforme. On obtient ainsi l'amélioration simultanée du RSB et du débit de transmission moyen

Lattice algorithm for adaptive stable identification and robust reconstruction of non stationary AR processes with missing observations

International audienceThis paper deals with the problem of adaptive reconstruction and identification of non stationary AR processes with randomly missing observations. Existent methods use a direct realization of the filter. Therefore, the estimated parameters may not correspond to a stable all-pole filter. In addition, when the probability of missing a sample is high, existent methods may converge slowly or even fail to converge. We propose, at our knowledge, the first algorithm based on the lattice structure for online processing of signals with missing samples. It is an extension of the RLSL algorithm to the case of missing observations, using a Kalman filter for the prediction of missing samples. The estimated parameters guarantee the stability of the corresponding all-pole filter. In addition it is robust to high probabilities of missing a sample. It offers a fast parameter tracking even for high probabilities of missing a sample. It is compared to the Kalman pseudo linear RLS algorithm, an already proposed algorithm using a direct realization of the filter. The proposed algorithm shows better performance in reconstruction of audio signals

New non-uniform transmission and ADPCM coding system for improving both signal to noise ratio and bit rate

International audienceHere we address the problem of adaptive digitaltransmission systems. New systems based on a nonuniform transmission (NUT) principle are proposed, utilizing a recently proposed algorithm for adaptive identification and reconstruction of AR processes subject to missing data. We propose a new adaptive sampling (nonuniform transmission) method combined with the adaptive reconstruction algorithm. A new NUT-ADPCM coding-decoding system is designed. The proposed system is demonstrated for audio-signal compression and compared to the ADPCM G.726 standard. The new system yields improvements in both signal-to-noise ratio and average bit rat

Algorithmes adaptatifs d'identification et de reconstruction de processus AR à échantillons manquants

On souhaite reconstruire en ligne des signaux à échantillons manquants en utilisant une approche paramétrique. On propose alors des algorithmes adaptatifs d identification et de reconstruction de processus AR à échantillons manquants. On s intéresse premièrement à l extension des algorithmes de gradient au cas des signaux à échantillons manquants. On propose alors deux alternatives à un algorithme existant fondées sur deux autres prédicteurs. Les algorithmes proposés convergent vers une estimation non biaisée des paramètres. Or les algorithmes de gradient souffrent d une faible vitesse de convergence. Pour cela, on s inte resse à l extension de l algorithme MCR au cas des signaux à échantillons manquants. On utilise alors l algorithme MCR pseudo-linéaire pour l identification conjointement avec un filtre de Kalman pour une prédiction optimale du signal au sens des moindres carrés. L algorithme résultant permet une identification non biaisée des paramètres. De plus, il est rapide et bien adapté à l identification de processus non stationnaires. Néanmoins, souhaitant contrôler la stabilité du filtre identifié, on s intéresse ensuite à une identification fondée sur une structure en treillis du filtre. Ainsi, on propose une extension de l algorithme de Burg adaptatif au cas des signaux à échantillons manquants, en utilisant pour la prédiction un filtre de Kalman. La stabilité du modèle ainsi identifié est garantie. De plus, l algorithme s adapte rapidement aux variations des paramètres. Finalement, on propose d utiliser les algorithmes proposés dans un système à transmission non uniforme. On obtient ainsi l amélioration simultanée du RSB et du débit de transmission moyen.We are concerned in online reconstruction of signals subject to missing samples using a parametric approach. We propose adaptive algorithms for identification and reconstruction of AR processes with missing samples. Firstly, we consider the extension of gradient algorithms to the case of signals with missing samples. We propose two alternatives to an existent algorithm based on two other predictors. The proposed algorithms converge toward unbiased estimation of the parameters. However, gradient algorithms suffer from slow convergence. Therefore, we consider the RLS algorithm extension to the case of signals subject to missing samples. We use jointly, the pseudo-linear RLS algorithm for the identification and a Kalman filter for optimal reconstruction of the signal in the least mean square sense. The estimated parameters, using the proposed algorithm, are unbiased. In addition, it is fast and well adapted to the identification of non stationary signals. Nevertheless, looking for the control of the identified filter stability, we propose to identify the signal using the lattice structure of the filter. We propose an extension of the Burg adaptive algorithm to the case of signals subject to missing observations, using a Kalman filter for the prediction. The estimated parameters guarantee the stability of the corresponding filter. In addition, it offers a faster tracking parameter. Finally, we use the proposed algorithms in non uniform transmission systems. We then get the improvement of both the SNR and the average transmission rate.ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF