Optimization-based design and implementation of multidimensional zero-phase IIR filters

IEEE Trans. Signal Process.

Kim

Beard

et al. 2009

Self Cite

Abstract-This paper considers estimation of pixel-wise monotonic increasing (or decreasing) data from a time series of noisy blurred images. The motivation comes from estimation of mechanical structure damage that accumulates irreversibly over time. We formulate a Maximum A posteriory Probablity (MAP) estimation problem and find a solution by direct numerical optimization of a log-likelihood index. Spatial continuity of the damage is modeled using a Markov Random Field (MRF). The MRF prior includes the temporal monotonicity constraints. We tune the MRF prior, using a spatial frequency domain loopshaping technique to achieve a tradeoff between noise rejection and signal restoration properties of the estimate.The MAP optimization is a large-scale Quadratic Programming (QP) problem that could have more than a million of decision variables and constraints. We describe and implement an efficient interior-point method for solving such optimization problem. The method uses a preconditioned conjugate gradient method to compute the search step. The developed QP solver relies on the special structure of the problem and can solve the problems of this size in a few tens of minutes, on a PC.The application example in the paper describes structural damage images obtained using a Structural Health Monitoring (SHM) system. The damage signal is distorted by environmental temperature that varies for each acquired image in the series. The solution for the experimental data is demonstrated to provide an excellent estimate of the damage accumulation trend while rejecting the spatial and temporal noise.Index Terms-Optimal estimation, spatio-temporal filtering, regularization, interior-point method, isotonic regression, Markov Random Field.

Section: B Design Of Regularization Operatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Estimation of Deterioration From Diagnostic Image Sequence

IEEE Trans. Signal Process.

Kim

Beard

et al. 2009

Self Cite

“…The distributed estimation is closely related to solution of distributed inverse problems such as deblurring in image processing and grid methods for solving partial differential equations. Formulations of image processing and multidimensional filtering problem related to this paper and further references could be found in [17], [20].…”

Section: Introductionmentioning

confidence: 99%

Design of Low-Bandwidth Spatially Distributed Feedback

IEEE Trans. Automat. Contr.

Boyd

Stein

2008

Abstract-The paper considers a family of linear timeinvariant and spatially-invariant (LTSI) systems that are both distributed and localized. The spatial responses of the distributed plant are localized in spatial neighborhoods of each location. The feedback computations are also distributed and the information flow is localized in a spatial neighborhood of each location. The feedback is aimed at controlling spatial distributions of variables in the systems with a relatively low bandwidth in the time direction. Such systems have many important applications including industrial processes, imaging systems, signal and image processing, and others.We describe a new method for designing (tuning) a certain family of low-bandwidth controllers for such plants. We consider LTSI controllers with a fixed structure, which is PID or similar low-bandwidth feedback in time and local in spatial coordinates. Two spatial feedback filters, symmetric and with finite spatial response, modify the local PID control signal by mixing in the error and control signals at nearby nodes. These two filters provide loopshaping and regularization of the spatial feedback loop. Like an ordinary PID controller, this controller structure is simple, but provides adequate performance in many practical settings.We cast a variety of specifications on the steady-state spatial response of the controller and its time response as a set of linear inequalities on the design variables, and so can carry out the design of the spatial filters using linear programming. The method handles steady-state limits on actuator signals, error signals, and several constraints related to robustness to plant and controller variation. The method allows handling the effects of boundary conditions and guaranteed closed-loop spatial or time decay. It does appear to work very well for low-bandwidth controllers, and so is applicable in a variety of practical situations.

“…Finally, Figure 4 illustrates optical transfer functions in the designed specifications for the update, those in (16), (18), (19 …”

Section: Implementation Examplementioning

confidence: 99%

“…This paper considers feedback in distributed estimation -a dual problem. A related multidimensional filter design work is [18].…”

Section: Introductionmentioning

confidence: 99%

Feedback Loop Design and Analysis for Iterative Localized Image Deblurring

Proceedings of the 44th IEEE Conference on Decision and Control

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Abstract-This paper considers image deblurring algorithm based on model-based iterative update of the image estimate. The update has two principal terms: (i) integral feedback of blurred image prediction error and (ii) feedback of the past deblurred image estimate. The two feedback terms are computed by applying two FIR operators. The paper shows how these feedback update operators can de designed with a given degree of localization to provide an optimal tradeoff between design objectives such as convergence speed, noise amplification, quality of image restoration, and robustness. The solution to the feedback operator design problem is obtained by Linear Programming optimization. A parallelized implementation of the update algorithm using localized feedback operators is scalable to very large image sizes.