The author consider the design of robust deconvolution filters for linear discrete time systems with stochastic parameter and noise uncertainties. It is assumed that some large but bounded uncertainties exist in the driving and measurement noise covariances as well as the second-order statistics of stochastic parameters and initial conditions. Three kinds of minimax sensitivity criteria are used to develop the techniques to the synthesis of minimax deconvolution filters under uncertain linear stochastic systems. Their approach is based on saddle-point theory and the sensitivity analysis of Kalman filters. The design algorithms give the recursive realization of the minimax deconvolution filters for the time-varying uncertain systems under fairly general conditions. For the time-invariant uncertain case the existence and solutions of steady-state deconvolution filters are further developed. Finally, the utility of the minimax design approaches and the properties of the resulting minimax deconvolution filters are illustrated by a numerical example. >

Minimax robust deconvolution filters under stochastic parametric and noise uncertainties

In this contribution, a generic applied evolutionary hybrid technique that combines the effectiveness of adaptive multimodel partitioning filters and genetic algorithm (GAs) robustness has been designed, developed, and applied in real-world adaptive system modeling and information mining problems. The method can be applied to linear and nonlinear real-world data, is not restricted to the Gaussian case, is computationally efficient, and is applicable to online/adaptive operation. Furthermore, it can be realized in a parallel processing fashion, a fact that makes it amenable to very large scale integration (VLSI) implementation.

A generic applied evolutionary hybrid technique

One objective of seismic signal processing is to identify the layered subsurface structure by sending seismic wavelets into the ground. This is a blind deconvolution process since the seismic wavelets are usually not measurable and therefore, the subsurface face layers are identified only by the reflected seismic signals. Conventional methods often approach this problem by making assumptions about the subsurface structures and/or the seismic wavelets. In this paper an alternative technique is presented. It applies blind channel identification methods to prestack seismic deconvolution. A unique feature of this proposed method is that no such assumptions are needed. In addition, it fits into the structure of current seismic data acquisition techniques, thus no extra cost is involved. Simulations on both synthetic and field seismic data demonstrate that it is a promising new method for seismic signal processing.

The application of blind channel identification techniques to prestack seismic deconvolution

A method for simultaneous autoregressive (AR) model order selection and identification is proposed, which is based on the adaptive Lainiotis filter (ALF). The method is not restricted to the Gaussian case, is applicable to online/adaptive operation, and is computationally efficient. It can be realized in a parallel processing fashion. The AR model order selection and identification problem is reformulated so that it can be fitted into the framework of a state space under uncertainty estimation problem framework. The ALF is briefly presented and its application to the specific problem is discussed. Simulation examples are presented to demonstrate the superior performance of the method in comparison with previously reported ones. >

AR model identification with unknown process order

A new method is proposed in this paper for sequential parameter estimation and deconvolution of seismic signals. An on-line algorithm of the instrumental variables method is appropriately combined for this purpose with a fixed-lag version of minimum-variance seismic deconvolution. A consistency and an accuracy analysis of the proposed algorithm are presented, using a special type of instrumental variables. The performance of the method is examined in the cases of nonminimum phase or slowly time-varying seismic wavelets. The results are illustrated by simulation studies using examples already studied in the literature.

An Instrumental Variable Approach to Minimum-Variance Seismic Deconvolution

The application of a recently proposed fast implementation of the recursive least squares algorithm, called the Fast Kalman Algorithm (FKA) to adaptive deconvolution of seismic data is discussed. The newly proposed algorithm does not require the storage and updating of a matrix to calculate the filter gain, and hence is computationally very efficient. Furthermore, it has an interesting structure yielding both the forward and backward prediction residuals of the seismic trace and thus permits the estimation of a ?smoothed residual? without any additional computations. The paper also compares the new algorithm with the conventional Kalman algorithm (CKA) proposed earlier [3] for seismic deconvolution. Results of experiments on simulated as well as real data show that while the FKA is a little more sensitive to the choice of some initial parameters which need to be selected carefully, it can yield comparable performance with greatly reduced computational effort.

On the Application of the Fast Kalman Algorithm to Adaptive Deconvolution of Seismic Data

This paper examines the results of the application of two lattice algorithm to the problem of adaptive deconvolution on non-stationary seismic data. A comparative study of the deconvolution performance of the recently proposed gradient lattice and least-squares lattice algorithms is made with the help of experiments on simulated and real seismic data. We show that the gradient lattice algorithm is computationally superior, but it suffers from a possible slow rate of convergence, while the least-squares lattice has better convergence properties and is more robust numerically. We also show that both algorithms can yield equally good deconvolution results with a moderate amount of computation. Finally we indicate that a modified deconvolved output, derived as a linear combination of the forward and backward residuals, improves the performance without involving any additional computational burden.

A. K. Mahalanabis

Papers

On the Application of the Fast Kalman Algorithm to Adaptive Deconvolution of Seismic Data

Deconvolution of nonstationary seismic data using adaptive lattice filters