Robust constrained deconvolution

Sekko, Edgard; Sarri, Patrick; Thomas, Gérard

doi:10.1109/icassp.1996.544215

Cited by 6 publications

(7 citation statements)

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“…where K is the stationary filter gain [20], Gelb [13]. Image Processing Theory, Tools and Applications The resolution of this problem applying the optimal control theory leads to the following result:…”

Section: Deconvolution Processmentioning

confidence: 99%

Deconvolution for slowly time-varying systems 3D cases

Zenati

Boukrouche

Neveux

2012

2012 3rd International Conference on Image Processing Theory, Tools and Applications (IPTA)

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In the present work, we discuss an extension of the deconvolution techniques of Sekko [20] and Neveux [18] to 3D signals. The signals are assumed to be degraded by electronic linear systems, in which parameters are slowly time-varying such as sensors or other storage systems. For this purpose, Sekko & al.[20] developed a structure that has been adapted to time-varying systems [18] in order to produce an inverse filter with constant gain. This latter method was applied successfully to ordinary images [23]. The treatment of omnidirectional images requires working on the unit sphere. Therefore, the problem should be cast in 3D. In the 3D case, the deconvolution method [18] can be applied after some manipulations. The Heinz-Hopf fibration offers the possibility to consider that the sphere is similar to a torus. The advantage of this approach is that Kalman filtering can be applied and omnidirectional images projected on the sphere can be deconvolved.

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Section: Deconvolution Processmentioning

confidence: 99%

Deconvolution for slowly time-varying systems 3D cases

Zenati

Boukrouche

Neveux

2012

2012 3rd International Conference on Image Processing Theory, Tools and Applications (IPTA)

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“…[2] for time-invariant systems, which was later improved by Neveux [3,4] in order to adapt it for time-varying processes. In the deconvolution method [2], the signal of measurement is corrupted by a system represented by a transfer function or a state equation. In the proposed procedure the deconvolution is undertaken by means of a trajectory tracking scheme.…”

mentioning

confidence: 99%

“…For this purpose, we will apply tools of filtering and robust optimal control to the structure used by [2] within the framework of linear certain systems. It is necessary for us to introduce both the robustness notion in the filtering sense and the signal estimation algorithm.…”

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confidence: 99%

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Deconvolution for uncertain systems

Zenati

Boukrouche

2009

2009 6th International Symposium on Mechatronics and Its Applications

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With matrices A e 9\n.n , Be 9\n.1 and C e 9\1.n. We denote x(/)e 9\n the state vector describing the system, u(t) the input signal to be restored, and Ym(t) is a noisy signal. The signals v](t) and V2(t) are random signals supposed to be white, zero mean uncorrelated Gaussian processes with covariance (Jv] and (Jv2' And the associated Kalman filter is given by:The gain of the stationary Kalman filter is given by:the positive symmetric matrix solution of the Algebraic Riccati Equation (ARE): AP+PA t -PCta:iCP+Bav1B t =0 (4) Let the augmented state vector be defined as: X (I) = [xp (I)]Xe (/) we then obtain the following augmented state equations:The deconvolution procedure developed by [2] is depicted by figurel.Figure 1. Deconvolution structure used by [2}.We have to find the signal u(t) minimizing: ABSTRACTWhere h(t) is the impulse response of the process and u(t) is the excitation. The inverse operation of recovering the signal u(t) fromy(t) and h(t), is called deconvolution. As one may find in the literature, this problem is known to be an ill-posed one [1]. To be more precise, the ideal solution is the inverse system but the presence of measurement noise does not allow a direct inversion. Meanwhile, an approximate inversion through the well-known regularization method can be easily obtained. We propose a deconvolution procedure based on the one developed by Sekko & al.[2] for time-invariant systems, which was later improved by Neveux [3,4] in order to adapt it for time-varying processes. In the deconvolution method [2], the signal of measurement is corrupted by a system represented by a transfer function or a state equation. In the proposed procedure the deconvolution is undertaken by means of a trajectory tracking scheme. We use the following state equations to represent the system under study: .Ym (I) = C.xp (I) + V2 (I)In control theory, the response of a process to an exciting signal is described by the following convolution product: +00 y(t) = fh(t-t') u(r) dt'(1)

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