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1. Stochastic Source Seeking for Mobile Robots in Obstacle Environments Via the SPSA Method.

Author

Ramirez-Llanos, Eduardo and Martinez, Sonia

Subjects
*ALGORITHMS, *MOBILE robots, *MATHEMATICAL optimization, *NUMERICAL analysis, *MATHEMATICAL analysis
Abstract

This paper considers a class of stochastic source-seeking problems to drive a mobile robot to the minimizer of a source signal. Our approach is first analyzed in an obstacle-free scenario, where measurements of the signal at the robot location and information of a contact sensor are required. We extend our results to environments with obstacles under mild assumptions on the step size. Our approach builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithms to a ball whose size depends on the step size that contains the location of the source. The novelty relies in that we consider nondifferentiable convex functions, a fixed step size, and the environment may contain obstacles. Our proof methods employ nonsmooth Lyapunov function theory, tools from convex analysis, and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithms in a two-dimensional scenarios. [ABSTRACT FROM AUTHOR]

Published
2019
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2. Alternating Direction Method for Balanced Image Restoration.

Author

Xie, Shoulie and Rahardja, Susanto

Subjects
*IMAGE reconstruction, *ALGORITHMS, *REGULARIZATION parameter, *HESSIAN matrices, *NUMERICAL analysis, *FRAMES (Vector analysis), *DECONVOLUTION (Mathematics), *MATHEMATICAL optimization
Abstract

This paper presents an efficient algorithm for solving a balanced regularization problem in the frame-based image restoration. The balanced regularization is usually formulated as a minimization problem, involving an \ell2 data-fidelity term, an \ell1 regularizer on sparsity of frame coefficients, and a penalty on distance of sparse frame coefficients to the range of the frame operator. In image restoration, the balanced regularization approach bridges the synthesis-based and analysis-based approaches, and balances the fidelity, sparsity, and smoothness of the solution. Our proposed algorithm for solving the balanced optimal problem is based on a variable splitting strategy and the classical alternating direction method. This paper shows that the proposed algorithm is fast and efficient in solving the standard image restoration with balanced regularization. More precisely, a regularized version of the Hessian matrix of the \ell2 data-fidelity term is involved, and by exploiting the related fast tight Parseval frame and the special structures of the observation matrices, the regularized Hessian matrix can perform quite efficiently for the frame-based standard image restoration applications, such as circular deconvolution in image deblurring and missing samples in image inpainting. Numerical simulations illustrate the efficiency of our proposed algorithm in the frame-based image restoration with balanced regularization. [ABSTRACT FROM AUTHOR]

Published
2012
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