The Experts below are selected from a list of 246 Experts worldwide ranked by ideXlab platform
Rick P. Millane - One of the best experts on this subject based on the ideXlab platform.
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bayesian estimation in an Image Restoration Problem in x ray fiber diffraction
International Conference on Acoustics Speech and Signal Processing, 1998Co-Authors: Subramanian Baskaran, Rick P. MillaneAbstract:The Restoration of an incomplete Image from a known part and experimental data in the form of the Fourier amplitude squared sums is formulated as a Bayesian estimation Problem. This Problem is motivated by the structure completion Problem in X-ray fiber diffraction analysis. An appropriate prior of uniformly distributed impulses is used. The Bayesian MMSE and MAP estimates are obtained. Simulations are used to compare the performance of the estimates. The results show that the MMSE estimate significantly outperforms the other estimates. The restored Images exhibit some bias towards the known part of the Image. This can be partly reduced by an unbiasing procedure.
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ICASSP - Bayesian estimation in an Image Restoration Problem in X-ray fiber diffraction
Proceedings of the 1998 IEEE International Conference on Acoustics Speech and Signal Processing ICASSP '98 (Cat. No.98CH36181), 1Co-Authors: Subramanian Baskaran, Rick P. MillaneAbstract:The Restoration of an incomplete Image from a known part and experimental data in the form of the Fourier amplitude squared sums is formulated as a Bayesian estimation Problem. This Problem is motivated by the structure completion Problem in X-ray fiber diffraction analysis. An appropriate prior of uniformly distributed impulses is used. The Bayesian MMSE and MAP estimates are obtained. Simulations are used to compare the performance of the estimates. The results show that the MMSE estimate significantly outperforms the other estimates. The restored Images exhibit some bias towards the known part of the Image. This can be partly reduced by an unbiasing procedure.
Aggelos K. Katsaggelos - One of the best experts on this subject based on the ideXlab platform.
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Spatially Adaptive Intensity Bounds for Image Restoration
EURASIP Journal on Advances in Signal Processing, 2003Co-Authors: Tania Stathaki, Aggelos K. KatsaggelosAbstract:Spatially-adaptive intensity bounds on the Image estimate are shown to be an effective means of regularising the ill-posed Image Restoration Problem. For blind Restoration, the local intensity constraints also help to further define the solution, thereby reducing the number of multiple solutions and local minima. The bounds are defined in terms of the local statistics of the Image estimate and a control parameter which determines the scale of the bounds. Guidelines for choosing this parameter are developed in the context of classical (nonblind) Image Restoration. The intensity bounds are applied by means of the gradient projection method, and conditions for convergence are derived when the bounds are refined using the current Image estimate. Based on this method, a new alternating constrained minimisation approach is proposed for blind Image Restoration. On the basis of the experimental results provided, it is found that local intensity bounds offer a simple, flexible method of constraining both the nonblind and blind Restoration Problems.
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Hyperparameter estimation in Image Restoration Problems with partially known blurs
Optical Engineering, 2002Co-Authors: Nikolaos P. Galatsanos, Rafael Molina, Vladimir Z. Mesarovic, Aggelos K. Katsaggelos, Javier MateosAbstract:This work is motivated by the observation that it is not pos- sible to reliably estimate simultaneously all the necessary hyperparam- eters in an Image Restoration Problem when the point-spread function is assumed to be the sum of a known deterministic and an unknown ran- dom component. To solve this Problem we propose to use gamma hy- perpriors for the unknown hyperparameters. Two iterative algorithms that simultaneously restore the Image and estimate the hyperparameters are derived, based on the application of evidence analysis within the hierar- chical Bayesian framework. Numerical experiments are presented that show the benefits of introducing hyperpriors for this Problem. © 2002 So-
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ICASSP - Multichannel Image Restoration using compound Gauss-Markov random fields
2000 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings (Cat. No.00CH37100), 2000Co-Authors: R. Molina, Javier Mateos, Aggelos K. KatsaggelosAbstract:A solution to the multichannel Image Restoration Problem is provided using compound Gauss-Markov random fields. For the single channel deblurring Problem the convergence of the simulated annealing (SA) and iterative conditional mode (ICM) algorithms has not been established. We propose two new iterative multichannel Restoration algorithms which can be considered as extensions of the classical SA and ICM approaches and whose convergence is established. Experimental results with color Images demonstrate the effectiveness of the proposed algorithms.
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Bayesian and regularization methods for hyperparameter estimation in Image Restoration
IEEE Transactions on Image Processing, 1999Co-Authors: Rafael Molina, Aggelos K. Katsaggelos, Javier MateosAbstract:In this paper, we propose the application of the hierarchical Bayesian paradigm to the Image Restoration Problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the Image Restoration Problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.
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Hierarchical Bayesian approach to Image Restoration and the iterative evaluation of the regularization parameter
Visual Communications and Image Processing '94, 1994Co-Authors: Rafael Molina, Aggelos K. KatsaggelosAbstract:In an Image Restoration Problem we usually have two different kinds of information. In the first stage, we have knowledge about the structural form of the noise and local characteristics of the Image. These noise and Image models normally depend on unknown hyperparameters. The hierarchical Bayesian approach adds a second stage by putting a hyperprior on these hyperparameters, through which information about these hyperparameters is included. In this work we relate the hierarchical Bayesian approach to Image Restoration to an iterative approach for estimating these hyperparameters in a deterministic way.
Subramanian Baskaran - One of the best experts on this subject based on the ideXlab platform.
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bayesian estimation in an Image Restoration Problem in x ray fiber diffraction
International Conference on Acoustics Speech and Signal Processing, 1998Co-Authors: Subramanian Baskaran, Rick P. MillaneAbstract:The Restoration of an incomplete Image from a known part and experimental data in the form of the Fourier amplitude squared sums is formulated as a Bayesian estimation Problem. This Problem is motivated by the structure completion Problem in X-ray fiber diffraction analysis. An appropriate prior of uniformly distributed impulses is used. The Bayesian MMSE and MAP estimates are obtained. Simulations are used to compare the performance of the estimates. The results show that the MMSE estimate significantly outperforms the other estimates. The restored Images exhibit some bias towards the known part of the Image. This can be partly reduced by an unbiasing procedure.
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ICASSP - Bayesian estimation in an Image Restoration Problem in X-ray fiber diffraction
Proceedings of the 1998 IEEE International Conference on Acoustics Speech and Signal Processing ICASSP '98 (Cat. No.98CH36181), 1Co-Authors: Subramanian Baskaran, Rick P. MillaneAbstract:The Restoration of an incomplete Image from a known part and experimental data in the form of the Fourier amplitude squared sums is formulated as a Bayesian estimation Problem. This Problem is motivated by the structure completion Problem in X-ray fiber diffraction analysis. An appropriate prior of uniformly distributed impulses is used. The Bayesian MMSE and MAP estimates are obtained. Simulations are used to compare the performance of the estimates. The results show that the MMSE estimate significantly outperforms the other estimates. The restored Images exhibit some bias towards the known part of the Image. This can be partly reduced by an unbiasing procedure.
Arnaud Lazare - One of the best experts on this subject based on the ideXlab platform.
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Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation
Journal of Global Optimization, 2021Co-Authors: Sourour Elloumi, Amélie Lambert, Arnaud LazareAbstract:We propose a method called Polynomial Quadratic Convex Reformulation ( PQCR ) to solve exactly unconstrained binary polynomial Problems (UBP) through quadratic convex reformulation. First, we quadratize the Problem by adding new binary variables and reformulating (UBP) into a non-convex quadratic program with linear constraints (MIQP). We then consider the solution of (MIQP) with a specially-tailored quadratic convex reformulation method. In particular, this method relies, in a pre-processing step, on the resolution of a semi-definite programming Problem where the link between initial and additional variables is used. We present computational results where we compare PQCR with the solvers Baron and Scip . We evaluate PQCR on instances of the Image Restoration Problem and the low auto-correlation binary sequence Problem from MINLPLib . For this last Problem, 33 instances were unsolved in MINLPLib . We solve to optimality 10 of them, and for the 23 others we significantly improve the dual bounds. We also improve the best known solutions of many instances.
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Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation
Journal of Global Optimization, 2020Co-Authors: Sourour Elloumi, Amélie Lambert, Arnaud LazareAbstract:We propose a solution approach for the Problem (P) of minimizing an unconstrained binary polynomial optimization Problem. We call this method PQCR (Polynomial Quadratic Convex Reformulation). The resolution is based on a 3-phase method. The first phase consists in reformulating (P) into a quadratic program (QP). For this, we recursively reduce the degree of (P) to two, by use of the standard substitution of the product of two variables by a new one. We then obtain a linearly constrained binary program. In the second phase, we rewrite the quadratic objective function into an equivalent and parametrized quadratic function using the equality x 2 i = x i and new valid quadratic equalities. Then, we focus on finding the best parameters to get a quadratic convex program which continuous relaxation's optimal value is maximized. For this, we build a semidefinite relaxation (SDP) of (QP). Then, we prove that the standard linearization inequalities, used for the quadratization step, are redundant in (SDP) in presence of the new quadratic equalities. Next, we deduce our optimal parameters from the dual optimal solution of (SDP). The third phase consists in solving (QP *), the optimal reformulated Problem, with a standard solver. In particular, at each node of the branch-and-bound, the solver computes the optimal value of a continuous quadratic convex program. We present computational results on instances of the Image Restoration Problem and of the low autocorrelation binary sequence Problem. We compare PQCR with other convexification methods, and with the general solver Baron 17.4.1 [39]. We observe that most of the considered instances can be solved with our approach combined with the use of Cplex [24].
Vladimir Viktorovich Volkov - One of the best experts on this subject based on the ideXlab platform.
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Recovering Images, Registered by Device with Inexact Point-Spread Function, Using Tikhonov’s Regularized Least Squares Method
International journal of artificial intelligence, 2015Co-Authors: V. I. Erokhin, Vladimir Viktorovich VolkovAbstract:The theoretical and practical aspects of using Tikhonov’s regularized least squares method to solve the Image Restoration Problem are considered. We suppose, that degraded Image was obtained from registering device with inexact point-spread function. The method of reducing Image Restoration Problem to Problem of solving approximate systems of linear algebraic equations and some matrix transformation of this systems are discussed. Both positive and negative values of regularization parameter are considered, which is not common practice in Tikhonov regularization. The results of computational experiments are given. This experiments shows that there are such conditions that leads to necessity of using negative regularization parameter in Tikhonov’s regularized least squares method.