H/sub ∞/ deconvolution filter design and its application in image restoration

Yu, Xianggang; Hsu, C.S.; Bamberger, R.H.; Reeves, Stanley J.

doi:10.1109/icassp.1995.480096

Cited by 11 publications

(8 citation statements)

References 4 publications

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“…To construct a fictitious second-order state-space model, we further calculate the following quadratic measurement output: [2] (i)w [2] [2] (i)w [2] (i).…”

Section: The Second-order Extended Systemmentioning

confidence: 99%

“…where the block matrices in (12)- (14) are [2] (i) st -1 Ψ w,4 -Ψ [2] w,2 D [2] [2] (i)E x [2] (i) E T x [2] (i) H [2] [2] (i + 1) = A [2] (i)E x [2] (i) + B [2]…”

Section: Lemmamentioning

confidence: 99%

“…During the last three decades, the estimation problem of input noise has become an active field in industry and has a wide range of applications in fault detection, petroleum prospecting, image restoration, speech processing, and so forth [1][2][3][4][5][6]. The Kalman deconvolution filter approach applied to the reflection coefficient sequence estimate in oil exploration was first proposed in [3].…”

Section: Introductionmentioning

confidence: 99%

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A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

Zhao

et al. 2020

Adv Differ Equ

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We investigate non-Gaussian noise second-order filtering and fixed-order smoothing problems for non-Gaussian stochastic discrete systems with packet dropouts. We present a novel Kalman-like nonlinear non-Gaussian noise estimation approach based on the packet dropout probability distribution and polynomial filtering technique. By means of properties of Kronecker product we first introduce a second-order polynomial extended system and then analyze the means and variances of the Kronecker powers of the extended system noises. To generate noise estimators in forms of filtering and smoothing, we use the innovation approach. We give an example to illustrate that the presented algorithm has better robustness against packet dropouts than conventional linear minimum variance estimation.

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“…To construct a fictitious second-order state-space model, we further calculate the following quadratic measurement output: [2] (i)w [2] [2] (i)w [2] (i).…”

Section: The Second-order Extended Systemmentioning

confidence: 99%

“…where the block matrices in (12)- (14) are [2] (i) st -1 Ψ w,4 -Ψ [2] w,2 D [2] [2] (i)E x [2] (i) E T x [2] (i) H [2] [2] (i + 1) = A [2] (i)E x [2] (i) + B [2]…”

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

Zhao

et al. 2020

Adv Differ Equ

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“…In recent years, H 1 filtering for SMJSs has been extensively studied, for example, [38,40], and the references therein. Conversely, H 1 deconvolution filtering is to design a filter to estimate the unknown input signal of a given systems utilizing available measurement [41][42][43][44]. Over the past decades, as the extension of H 1 filtering, H 1 deconvolution filtering has been an important issue and widely used in many fields such as signal processing, image restoration, data transmission, nondestructive evaluation, reverberation cancellation, and so on [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

H_∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

et al. 2016

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This article investigates the problem of H 1 deconvolution filtering for a kind of uncertain descriptor hybrid system with state time-varying delays, limited communication capacity, and partially unknown transition rates. The limited communication capacity including signal transmission delays and data packet dropout. Mode-dependent and delay-dependent conditions are obtained by constructing a comprehensive stochastic Lyapunov-Krasovskii functional, which ensure the filtering error system is not only stochastically admissible but also satisfies a prescribed H 1 -norm level for all admissible uncertainties, signal transmission delays, and data packet dropout. The linear matrix inequalities technique is utilized to acquire the desired deconvolution filter parameters. An electrical RLC circuit example and two numerical examples are provided to demonstrate the usefulness and effectiveness of our methods.

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“…As the extension of H ∞ filter design, H ∞ deconvolution filter design problem has been an important research topic over the past years. Note that the H ∞ deconvolution filtering technique can be used in fault detection, image restoration, signal processing, data transmission, and other areas . In essence, the deconvolution filtering problem is to design a filter to estimate the unknown input signal of a system using available measurements.…”

Section: Introductionmentioning

confidence: 99%

Robust H_∞ deconvolution filtering for uncertain singular Markovian jump systems with time‐varying delays

Zhuang

Zhang

et al. 2015

Intl J Robust & Nonlinear

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SUMMARYThe problem of H 1 deconvolution filter design for a class of singular Markovian jump systems with time-varying delays and parameter uncertainties is considered in this paper. By constructing a more comprehensive stochastic Lyapunov-Krasovskii functional, novel delay-dependent conditions are established to guarantee the filtering error system is not only stochastically admissible, but also satisfies a prescribed H 1 -norm level for all admissible uncertainties. The desired filter parameters can be obtained by solving a set of strict linear matrix inequalities. Two examples and an electrical RLC circuit example are employed to verify the effectiveness and usefulness of the proposed methods in the paper.

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H/sub ∞/ deconvolution filter design and its application in image restoration

Cited by 11 publications

References 4 publications

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

H_∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

Robust H_∞ deconvolution filtering for uncertain singular Markovian jump systems with time‐varying delays

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H/sub ∞/ deconvolution filter design and its application in image restoration

Cited by 11 publications

References 4 publications

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

H∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

Robust H∞ deconvolution filtering for uncertain singular Markovian jump systems with time‐varying delays

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H_∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

Robust H_∞ deconvolution filtering for uncertain singular Markovian jump systems with time‐varying delays