We study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions of the Fourier samples of the ground ...
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We study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions of the Fourier samples of the ground truth up to a maximum cutoff frequency Kc. The reconstruction task is specified as an optimization problem with total-variation (TV) regularization (in the sense of measures) involving the Mth order derivative regularization operator L = DM. The order M >= 1 determines the degree of the reconstructed piecewise-polynomial spline, whereas the TV regularization norm, which is known to promote sparsity, guarantees a small number of pieces. We show that the solution of our optimization problem is always unique, which, to the best of our knowledge, is a first for TV-based problems. Moreover, we show that this solution is a periodic spline matched to the regularization operator L whose number of knots is upper-bounded by 2Kc. We then consider the grid-based discretization of our optimization problem in the space of uniform L-splines. On the theoretical side, we show that any sequence of solutions of the discretized problem converges uniformly to the unique solution of the gridless problem as the grid size vanishes. Finally, on the algorithmic side, we propose a B-spline-based algorithm to solve the discretized problem, and we demonstrate its numerical feasibility experimentally. On both of these aspects, we leverage the uniqueness of the solution of the original problem.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
With the continuous development of science and technology, automobile autonomous driving technology has gradually become a research hotspot. Among them, path planning and optimization technology is the key link to rea...
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With the continuous development of science and technology, automobile autonomous driving technology has gradually become a research hotspot. Among them, path planning and optimization technology is the key link to realizing automatic driving. This paper aims to discuss the path planning and optimization technology in automotive autonomous driving, analyze its current situation and development trend, and verify its effect through experiments. The role of path planning in our lives is very much needed and very *** path planning and optimization techniques can effectively improve the autonomous driving performance of vehicles. Reduce traffic accidents and improve safety and *** the ongoing route optimization research, autonomous driving technology will also be widely promoted and applied.
For large-scale distributed interactive simulation, it is important and difficult for data to communicate among thousands of objects. The purpose of the Data Distribution Management (DDM) service performs data filter ...
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ISBN:
(纸本)9783037853191
For large-scale distributed interactive simulation, it is important and difficult for data to communicate among thousands of objects. The purpose of the Data Distribution Management (DDM) service performs data filter and reduces irrelevant data between federations. grid-based algorithm can only manage to filter part of irrelevant data. Experimental results show that, compare with normal grid-based algorithms, the dynamic multicast method can minimize.
This paper describes a methodology to extract fuzzy models that describe linguistically the low-level features of an image (such as color, texture, etc.). The methodology combines grid-based algorithms with clustering...
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ISBN:
(纸本)9781424469208
This paper describes a methodology to extract fuzzy models that describe linguistically the low-level features of an image (such as color, texture, etc.). The methodology combines grid-based algorithms with clustering and tabular simplification methods to compress image information into a small number of fuzzy rules with high linguistic meaning. All the steps of the methodology are carried out with the help offered by the tools of Xfuzzy 3 environment, so we can define, simplify, tune and verify the fuzzy models automatically. Several examples are included to illustrate the advantages of the methodology.
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