Gérard Thomas

A deconvolution technique using optimal Wiener filtering and regularization

Abstract This paper describes a modified version of classical regularization techniques. Instead of using regularization in order to reduce the measurement noise effect of cancelling the inverse filter singularities, and to restore the original signal, a prefiltering is performed before the regularization. This prefiltering is obtained by using a Wiener filter based on a particular modelization of the signal to be restored. This new procedure is illustrated by the restoration of the Hubble Space Telescope (HST) images.

Robust Filtering for Linear Time-Invariant Continuous Systems

The problem of robust filtering for linear time-invariant (LTI) continuous systems subject to parametric uncertainties is treated in this paper through transfer function and polynomial representations, and then in the state-space domain. The basic idea consists of introducing the gradient of the estimation error with respect to the uncertain parameters in the optimization scheme via a epsiv-contaminated model. The general solution to the problem is given in the transfer function representation while, in the polynomial framework, the causal estimator is obtained by means of a spectral factorization and a Diophantine equation. The state-space realization of the causal estimator is discussed. Examples show the ability of the proposed technique to provide a reliable estimation in presence of model uncertainty.

A positive optimal deconvolution procedure

This paper deals with a modified version of the optimal deconvolution procedure that we have previously proposed in 1980. The restoration is considered as a tracking problem solved by application of the optimal control theory. For lack of constraint on the signal to be restored, we have shown that an analytical solution exists. We expose here an iterative version of this procedure in order to include constraints on the restored signal.

A modified version of Van-Cittert's iterative deconvolution procedure

It is well known that the iterative procedure of deconvolution proposed by Van-Cittert does not converge in every case. This correspondence gives a modified version of this method which converges for a broader class of distortions and removes some artifacts introduced by the original algorithm.

A constrained iterative deconvolution technique with an optimal filtering: application to a hydrocarbon concentration sensor

A deconvolution method for estimating unburned hydrocarbon concentration in boiler smokes is presented. In order to qualify a boiler regarding to the ecological European Standards an iterative constrained estimation algorithm including a filtering step has been set up. The application of such technique to both synthetic signals and experimental data has shown its robustness in regard to measurement noise and its reliability to restore a signal.

Robust constrained deconvolution

The problem of deconvolution of a signal distorted by a linear time-invariant system is considered. In order to regularise this ill-posed problem; we combined the use of optimal filter, the game theory approach applied to the tracking problem and the priori knowledge such as positivity on the restored signal. To illustrate the robustness of the exposed procedure, two numerical examples are given.

The

The Hinfin smoothing problem for continuous systems is treated in a state space representation by means of variational calculus techniques. The smoothing problem is introduced in an Hinfin criterion by means of an artificial discontinuity that splits the problem in term of Hinfin forward and Hinfin backward filtering problems. Hence, the smoother design is realized in three steps. First, a forward filter is developed. Secondly, a backward filter is developed taking into account the backward Markovian model. The third step consists of combining the two previous steps in order to compute the Hinfin smoothed estimate. An example shows the efficiency of this proposed smoother

H_infty

Abstract We propose an application of penalty functions and Lagrangian multipliers method to the constrained deconvulution. In order to illustrate the efficiency of the exposed procedures, a numerical example is given and results of the procedures exposed here are compared with those obtained by the Prost and Goutte algorithm.

Fixed-Interval Smoothing Problem for Continuous Systems

Abstract The deconvolution problem is considered in this paper as an application of the optimal control theory. After the presentation of the inverse convolution in the free noise case, its application in the presence of noise is developed using the concepts of optimal filtering.

Iterative constrained deconvolution

In this paper, we propose a deconvolution method based on discrete-time optimal control. By combining Kalman filtering with optimal control, we state the problem in terms of a tracking problem. This leads to solve a set of recurrent equations, including in particular a matrix Riccati equation. We present a method that transforms the solution of these recurrent equations in that of a linear system of equations. Once the linear system has been set up, the deconvolution procedure becomes very fast, and permits on-line deconvolution. It is also possible to use the discrete impulse response, and perform blind deconvolution. This technique includes an L/sub 2/ or H/sub /spl infin// optimal filter. Numerical examples illustrate the robustness of the procedure.