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In this paper, a motion-compensated de-interlacing algorithm using the Markov random field (MRF) model is proposed. The de-interlacing problem is formulated as a maximum a posteriori (MAP) MRF problem. The MAP solution is the one that minimizes an energy function, which imposes discontinuity-adaptive smoothness (DAS) spatial constraint on the de-interlaced frame. The edge direction information, which is used to formulate the DAS constraint, is implicitly indicated by weight vectors (weights for 16 digitized directions). Generally, large weights are assigned to along-edge directions and relatively small weights are assigned to across-edge directions. As a local statistical-based method, the proposed weighting method should be more robust than traditional edge-directed interpolation methods in deciding local edge directions. The proposed algorithm is implemented by an iterative optimization process, which guarantees convergence. However, a global optimal solution is not guaranteed due to computational complexity concern. Simulation results compare the proposed algorithm to other motion compensated de-interlacing algorithms. Significant improvements of de-interlaced edges are observed. [ABSTRACT FROM AUTHOR]

The proper choice of mapping used in space-mapping optimization algorithms is typically problem dependent. The number of parameters of the space-mapping surrogate model must be adjusted so that the model is flexible enough to reflect the features of the fine model, but at the same time is not over flexible. Its extrapolation capability should allow the prediction of the fine model response in the neighborhood of the current iteration point. A wrong choice of space-mapping type may lead to poor performance of the space-mapping optimization algorithm. In this paper, we consider a space-mapping optimization algorithm with an adaptive surrogate model. This allows us to adjust the type of space-mapping surrogate model used in a given iteration based on the approximation/extrapolation capability of the model. The technique does not require any additional fine model evaluations. [ABSTRACT FROM AUTHOR]

We consider the optimal control of mechanical systems on Lie groups and develop numerical methods that exploit the structure of the state space and preserve the system motion invariants. Our approach is based on a coordinate-free variational discretization of the dynamics that leads to structure-preserving discrete equations of motion. We construct necessary conditions for optimal trajectories that correspond to discrete geodesics of a higher order system and develop numerical methods for their computation. The resulting algorithms are simple to implement and converge to a solution in very few iterations. A general software implementation is provided and applied to two example systems: an underactuated boat and a satellite with thrusters. [ABSTRACT FROM AUTHOR]

A reconstruction algorithm is detailed for three-dimensional full-vectorial microwave imaging based on Newton-type optimization. The goal is to reconstruct the three-dimensional complex pemittivity of a scatterer in a homogeneous background from a number of time-harmonic scattered field measurements. The algorithm combines a modified Gauss—Newton optimization method with a computationally efficient forward solver, based on the fast Fourier transform method and the marching-on-in-source-position extrapolation procedure. A regularized cost function is proposed by applying a multiplicative-additive regularization to the least squares datafit. This approach mitigates the effect of measurement noise on the reconstruction and effectively deals with the non-linearity of the optimization problem. It is furthermore shown that the modified Gauss—Newton method converges much faster than the Broyden—Fletcher—Goldfarb—Shanno quasi-Newton method. Promising quantitative reconstructions from both simulated and experimental data are presented. The latter data are bi-static polarimetric free-space measurements provided by Institut Fresnel, Marseille, France. [ABSTRACT FROM AUTHOR]

In this brief, we consider extracting generalized eigenvectors in parallel for the generalized eigendecomposition problem. The problem is formulated as an optimization problem of minimizing an unconstrained quartic cost function based on the weighted rule. It is shown that the proposed weighted cost function has a unique global minimum, which corresponds to the principal generalized eigenvectors. In order to estimate the principal generalized eigenvector matrix efficiently, we simplify the quartic cost function as a quadric one by making an appropriate approximation, and then derive a fast algorithm for extracting the principal generalized eigenvector in parallel. We also show the application of the proposed algorithm in blind source separation. Numerical simulations are performed, and the results demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]