In this paper, we are interested in texture modeling with functional analysis spaces. We focus on the case of color image processing, and in particular color image decomposition. The problem of image decomposition con...
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In this paper, we are interested in texture modeling with functional analysis spaces. We focus on the case of color image processing, and in particular color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v. u should contain the geometric information of the original image, while v should be made of the oscillating patterns of f, such as textures. We propose here a scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. We provide a direct convergence proof of the scheme, and we give some analysis on color texture modeling.
A projected gradient algorithm (PGA) which is derived from the majorization-minimization (MM) framework has been proposed recently for Hessian-matrix Frobenius norm regularization image restoration model so that it cu...
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ISBN:
(纸本)9781479949557
A projected gradient algorithm (PGA) which is derived from the majorization-minimization (MM) framework has been proposed recently for Hessian-matrix Frobenius norm regularization image restoration model so that it currently provides state-of-the-art performance. Outside the MM framework and for the sake of further accelerating the convergence speed, this paper presents an efficient algorithm for image restoration under the Hessian-matrix Frobenius norm regularization. Using variable splitting to obtain an equivalent constrained optimization formulation, then our algorithm is addressed with an augmented Lagrangian method. Under the alternating direction method of multipliers (ADMM) framework, a fast algorithm with split augmented Lagrangian shrinkage scheme is thus proposed for image restoration. Finally, experimental results demonstrate that our algorithm achieves better results than PGA in terms of peak signal to noise ratio (PSNR) and convergence rate.
Image fusion is an important technique in remote sensing, as it could effectively combine the high spatial and the high spectral resolutions in order to obtain the complete and accurate description of the observed sce...
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Image fusion is an important technique in remote sensing, as it could effectively combine the high spatial and the high spectral resolutions in order to obtain the complete and accurate description of the observed scene. To date, many image fusion techniques have been developed. However, the available methods could hardly produce the satisfactory results in dealing with the fusion between the hyperspectral image and panchromatic image, especially in the spectral aspect. Therefore, in this paper, a new fusion approach, called unmixing-based constrained nonnegative matrix factorization (UCNMF), is proposed. This approach uses the NMF unmixing technique to generate the abundance matrix and uses the panchromatic image to sharpen the the material maps. The constrained term aiming at preserving the spectral information is added and the fusion problem is turned into a constrained optimization problem. Additionally, a projected gradient algorithm aiming at get the numerical solution of the optimization problem is presented. Finally, three groups of experiments are given to demonstrate that the proposed fusion method could be recognized as an effective technique in hyperspectral image fusion. (C) 2012 Elsevier GmbH. All rights reserved.
We study and solve a particular stochastic version of the Restricted Shortest Path Problem, the Stochastic Shortest Path Problem with Delay Excess Penalty. While arc costs are kept deterministic, arc delays are assume...
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This work deals with color image processing, with a focus on color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v = f - u. u contains the ...
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ISBN:
(纸本)9783642022555
This work deals with color image processing, with a focus on color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v = f - u. u contains the geometric information of the original image, while v is made of the oscillating patterns of f such as textures. We propose a numerical scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. A direct convergence proof of the scheme is provided, and some analysis on color texture modeling is given.
In this paper we describe and analyze an algorithm for certain box constrained optimization problems that may have several local minima. A paradigm for these problems is one in which the function to be minimized is th...
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In this paper we describe and analyze an algorithm for certain box constrained optimization problems that may have several local minima. A paradigm for these problems is one in which the function to be minimized is the sum of a simple function, such as a convex quadratic, and high frequency, low amplitude terms that cause local minima away from the global minimum of the simple function. Our method is gradient based and therefore the performance can be improved by use of quasi-Newton methods.
Methods related to Wolfe's recursive method for the resolution of degeneracy in linear programming are discussed, and a nonrecursive variant which works with probability one suggested. Numerical results for both n...
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The idea of continuation applied to the proximal transform of a polyhedral convex function is used to develop a general procedure for the construction of descent algorithms which has the property that it specializes t...
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The idea of continuation applied to the proximal transform of a polyhedral convex function is used to develop a general procedure for the construction of descent algorithms which has the property that it specializes to variants of the projectedgradient method when applied to such problems as $l_1 $ and $l_\infty $ curve fitting and linear programming. The novelty in this approach lies in the application of a generic form for the subdifferential of a polyhedral convex function which provides an explicit representation in terms of a small number of parameters. This is illustrated by applications to $l_\infty $ curve fitting and the minimization of piecewise linear functions, and these examples serve to establish the feasibility of a unified approach. The power of the method is demonstrated by deriving an effective algorithm for the rank regression problem (the existence of such an algorithm makes practical the application of nonparametric procedures based on rank in robust estimation). The new approach also opens up the possibility of common implementation strategies, and a tableau like scheme is decribed based on the use of orthogonal matrix factorizations.
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