The Experts below are selected from a list of 4830 Experts worldwide ranked by ideXlab platform
Mila Nikolova - One of the best experts on this subject based on the ideXlab platform.
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description of the Minimizers of least squares regularized with ell_0 norm uniqueness of the Global Minimizer
Siam Journal on Imaging Sciences, 2013Co-Authors: Mila NikolovaAbstract:We have an $\sf{M}\times\sf{N}$ real-valued arbitrary matrix $A$ (e.g., a dictionary) with $\sf{M} 0$. For several decades, this objective has attracted a ceaseless effort to conceive algorithms approaching a good Minimizer. Our theoretical contributions, summarized below, shed new light on the existing algorithms and can help in the conception of innovative numerical schemes. Solving the normal equation associated with any $\sf{M}$-row submatrix of $A$ is equivalent to computing a local Minimizer $\hat u$ of ${\mathcal{F}}_d$. (Local) Minimizers $\hat u$ of ${\mathcal{F}}_d$ are strict if and only if the submatrix, composed of those columns of $A$ wh...
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Description of the Minimizers of least squares regularized with L0-norm. Uniqueness of the Global Minimizer
SIAM Journal on Imaging Sciences, 2013Co-Authors: Mila NikolovaAbstract:We have an M x N real-valued arbitrary matrix A (e.g. a dictionary) with M0. For several decades, this objective has attracted a ceaseless effort to conceive algorithms approaching a good Minimizer. Our theoretical contributions, summarized below, shed new light on the existing algorithms and can help the conception of innovative numerical schemes. To solve the normal equation associated with any M-row submatrix of A is equivalent to compute a local Minimizer u* of F. (Local) Minimizers u* of F are strict if and only if the submatrix, composed of those columns of A whose indexes form the support of u*, has full column rank. An outcome is that strict local Minimizers of F are easily computed without knowing the value of b. Each strict local Minimizer is linear in data. It is proved that F has Global Minimizers and that they are always strict. They are studied in more details under the (standard) assumption that rank(A)=Mb_k, k
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description of the Minimizers of least squares regularized with bm ell_0 norm uniqueness of the Global Minimizer
arXiv: Numerical Analysis, 2013Co-Authors: Mila NikolovaAbstract:We have an $\m\x\n$ real-valued arbitrary matrix $A$ (e.g. a dictionary) with $\m 0$. For several decades, this objective has attracted a ceaseless effort to conceive algorithms approaching a good Minimizer. Our theoretical contributions, summarized below, shed new light on the existing algorithms and can help the conception of innovative numerical schemes. To solve the normal equation associated with any $\m$-row submatrix of $A$ is equivalent to compute a local Minimizer $\hu$ of $\Fd$. (Local) Minimizers $\hu$ of $\Fd$ are strict if and only if the submatrix, composed of those columns of $A$ whose indexes form the support of $\hu$, has full column rank. An outcome is that strict local Minimizers of $\Fd$ are easily computed without knowing the value of $\be$. Each strict local Minimizer is linear in data. It is proved that $\Fd$ has Global Minimizers and that they are always strict. They are studied in more details under the (standard) assumption that $\rank(A)=\m \be_\k$, all Global Minimizers of $\Fd$ are $\k$-sparse. An assumption on $A$ is adopted and proved to fail only on a closed negligible subset. Then for all data $d$ beyond a closed negligible subset, the objective $\Fd$ for $\be>\be_\k$, $\k\leq\m-1$, has a unique Global Minimizer and this Minimizer is $\k$-sparse. Instructive small-size ($5\x 10$) numerical illustrations confirm the main theoretical results.
Csaba Vincze - One of the best experts on this subject based on the ideXlab platform.
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A Robbins–Monro-type algorithm for computing Global Minimizer of generalized conic functions
Optimization, 2014Co-Authors: Matyas Barczy, Ábris Nagy, Csaba Noszály, Csaba VinczeAbstract:We generalize the notion and some properties of the conic function introduced by Vincze and Nagy in 2012. We provide a stochastic algorithm for computing the Global Minimizer of generalized conic functions, we prove almost sure and -convergence of this algorithm.
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A stochastic algorithm for computing Global Minimizer of generalized conic functions
arXiv: Optimization and Control, 2013Co-Authors: Matyas Barczy, Ábris Nagy, Csaba Noszály, Csaba VinczeAbstract:We generalize the notion and some properties of the conic function introduced by Vincze and Nagy (2012). We provide a stochastic algorithm for computing the Global Minimizer of generalized conic functions, we prove almost sure and L^q-convergence of this algorithm.
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A Robbins-Monro type algorithm for computing Global Minimizer of generalized conic functions
arXiv: Optimization and Control, 2013Co-Authors: Matyas Barczy, Ábris Nagy, Csaba Noszály, Csaba VinczeAbstract:We generalize the notion and some properties of the conic function introduced by Vincze and Nagy (2012). We provide a stochastic algorithm for computing the Global Minimizer of generalized conic functions, we prove almost sure and L^q-convergence of this algorithm.
R L Somorjai - One of the best experts on this subject based on the ideXlab platform.
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applicability of the method of smoothed functionals as a Global Minimizer for model polypeptides
The Journal of Physical Chemistry, 1992Co-Authors: H L Gordon, R L SomorjaiAbstract:The technique of smoothed functionals has been shown to be an efficient way to locate the Global minimum of certain functions. This makes it attractive as a prospective Global Minimizer for multidimensional, multiextremal functions. One such important application would be to use smoothed functionals to find the Global minimum in U, the total potential energy of an arbitrary protein. The Global minimum of U is conventionally assumed to correspond to the native structure of the protein
Matyas Barczy - One of the best experts on this subject based on the ideXlab platform.
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A Robbins–Monro-type algorithm for computing Global Minimizer of generalized conic functions
Optimization, 2014Co-Authors: Matyas Barczy, Ábris Nagy, Csaba Noszály, Csaba VinczeAbstract:We generalize the notion and some properties of the conic function introduced by Vincze and Nagy in 2012. We provide a stochastic algorithm for computing the Global Minimizer of generalized conic functions, we prove almost sure and -convergence of this algorithm.
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A stochastic algorithm for computing Global Minimizer of generalized conic functions
arXiv: Optimization and Control, 2013Co-Authors: Matyas Barczy, Ábris Nagy, Csaba Noszály, Csaba VinczeAbstract:We generalize the notion and some properties of the conic function introduced by Vincze and Nagy (2012). We provide a stochastic algorithm for computing the Global Minimizer of generalized conic functions, we prove almost sure and L^q-convergence of this algorithm.
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A Robbins-Monro type algorithm for computing Global Minimizer of generalized conic functions
arXiv: Optimization and Control, 2013Co-Authors: Matyas Barczy, Ábris Nagy, Csaba Noszály, Csaba VinczeAbstract:We generalize the notion and some properties of the conic function introduced by Vincze and Nagy (2012). We provide a stochastic algorithm for computing the Global Minimizer of generalized conic functions, we prove almost sure and L^q-convergence of this algorithm.
Thomas Guerrero - One of the best experts on this subject based on the ideXlab platform.
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Computing Global Minimizers to a constrained B‐spline image registration problem from optimal l1 perturbations to block match data
Medical physics, 2014Co-Authors: Edward M. Castillo, Richard Castillo, David Fuentes, Thomas GuerreroAbstract:Block matching is a well-known strategy for estimating corresponding voxel locations between a pair of images according to an image similarity metric. Though robust to issues such as image noise and large magnitude voxel displacements, the estimated point matches are not guaranteed to be spatially accurate. However, the underlying optimization problem solved by the block matching procedure is similar in structure to the class of optimization problem associated with B-spline based registration methods. By exploiting this relationship, the authors derive a numerical method for computing a Global Minimizer to a constrained B-spline registration problem that incorporates the robustness of block matching with the Global smoothness properties inherent to B-spline parameterization. The method reformulates the traditional B-spline registration problem as a basis pursuit problem describing the minimall1-perturbation to block match pairs required to produce a B-spline fitting error within a given tolerance. The sparsity pattern of the optimal perturbation then defines a voxel point cloud subset on which the B-spline fit is a Global Minimizer to a constrained variant of the B-spline registration problem. As opposed to traditional B-spline algorithms, the optimization step involving the actual image data is addressed by block matching. The performance of the method is measured in terms of spatial accuracy using ten inhale/exhale thoracic CT image pairs (available for download atwww.dir-lab.com) obtained from the COPDgene dataset and corresponding sets of expert-determined landmark point pairs. The results of the validation procedure demonstrate that the method can achieve a high spatial accuracy on a significantly complex image set. The proposed methodology is demonstrated to achieve a high spatial accuracy and is generalizable in that in can employ any displacement field parameterization described as a least squares fit to block match generated estimates. Thus, the framework allows for a wide range of image similarity block match metric and physical modeling combinations. © 2014 American Association of Physicists in Medicine.