Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals
cc-by An example of inverse estimation of irregular multivariable signals is provided by picture restoration. Pictures typically have sharp edges and therefore will be modeled by functions with discontinuities, and they could be blurred by motion. Mathematically, this means that we actually observe...
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fttexastechuniv:oai:ttu-ir.tdl.org:2346/95705 2023-09-26T15:21:00+02:00 Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals Chandrawansa, Kumari (TTU) Ruymgaart, Frits H. (TTU) Van Rooij, Arnoud C.M. 2000 application/pdf https://hdl.handle.net/2346/95705 https://doi.org/10.1155/S1048953300000010 eng eng Chandrawansa, K., Ruymgaart, F.H., & Van, Rooij, A.C.M. 2000. Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals. Journal of Applied Mathematics and Stochastic Analysis, 13(1). https://doi.org/10.1155/S1048953300000010 https://doi.org/10.1155/S1048953300000010 https://hdl.handle.net/2346/95705 Cesàro Integral Means Deconvolution Gibbs Phenomenon Hausdorff Metric Irregular Multivariable Input Signals Overshooting Speed of Convergence Article 2000 fttexastechuniv https://doi.org/10.1155/S1048953300000010 2023-08-26T22:07:06Z cc-by An example of inverse estimation of irregular multivariable signals is provided by picture restoration. Pictures typically have sharp edges and therefore will be modeled by functions with discontinuities, and they could be blurred by motion. Mathematically, this means that we actually observe the convolution of the irregular function representing the picture with a spread function. Since these observations will contain measurement errors, statistical aspects will be pertinent. Traditional recovery is corrupted by the Gibbs phenomenon (i.e., overshooting) near the edges, just as in the case of direct approximations. In order to eliminate these undesirable effects, we introduce an integral Cesàro mean in the inversion procedure, leading to multivariable Fejér kernels. Integral metrics are not sufficiently sensitive to properly assess the quality of the resulting estimators. Therefore, the performance of the estimators is studied in the Hausdorff metric, and a speed of convergence of the Hausdorff distance between the graph of the input signal and its estimator is obtained. ©2000 by North Atlantic Science Publishing Company. Article in Journal/Newspaper North Atlantic Texas Tech University: TTU DSpace Repository Journal of Applied Mathematics and Stochastic Analysis 13 1 1 14 |
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Open Polar |
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Texas Tech University: TTU DSpace Repository |
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fttexastechuniv |
language |
English |
topic |
Cesàro Integral Means Deconvolution Gibbs Phenomenon Hausdorff Metric Irregular Multivariable Input Signals Overshooting Speed of Convergence |
spellingShingle |
Cesàro Integral Means Deconvolution Gibbs Phenomenon Hausdorff Metric Irregular Multivariable Input Signals Overshooting Speed of Convergence Chandrawansa, Kumari (TTU) Ruymgaart, Frits H. (TTU) Van Rooij, Arnoud C.M. Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals |
topic_facet |
Cesàro Integral Means Deconvolution Gibbs Phenomenon Hausdorff Metric Irregular Multivariable Input Signals Overshooting Speed of Convergence |
description |
cc-by An example of inverse estimation of irregular multivariable signals is provided by picture restoration. Pictures typically have sharp edges and therefore will be modeled by functions with discontinuities, and they could be blurred by motion. Mathematically, this means that we actually observe the convolution of the irregular function representing the picture with a spread function. Since these observations will contain measurement errors, statistical aspects will be pertinent. Traditional recovery is corrupted by the Gibbs phenomenon (i.e., overshooting) near the edges, just as in the case of direct approximations. In order to eliminate these undesirable effects, we introduce an integral Cesàro mean in the inversion procedure, leading to multivariable Fejér kernels. Integral metrics are not sufficiently sensitive to properly assess the quality of the resulting estimators. Therefore, the performance of the estimators is studied in the Hausdorff metric, and a speed of convergence of the Hausdorff distance between the graph of the input signal and its estimator is obtained. ©2000 by North Atlantic Science Publishing Company. |
format |
Article in Journal/Newspaper |
author |
Chandrawansa, Kumari (TTU) Ruymgaart, Frits H. (TTU) Van Rooij, Arnoud C.M. |
author_facet |
Chandrawansa, Kumari (TTU) Ruymgaart, Frits H. (TTU) Van Rooij, Arnoud C.M. |
author_sort |
Chandrawansa, Kumari (TTU) |
title |
Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals |
title_short |
Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals |
title_full |
Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals |
title_fullStr |
Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals |
title_full_unstemmed |
Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals |
title_sort |
controlling the gibbs phenomenon in noisy deconvolution of irregular multivariable input signals |
publishDate |
2000 |
url |
https://hdl.handle.net/2346/95705 https://doi.org/10.1155/S1048953300000010 |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_relation |
Chandrawansa, K., Ruymgaart, F.H., & Van, Rooij, A.C.M. 2000. Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals. Journal of Applied Mathematics and Stochastic Analysis, 13(1). https://doi.org/10.1155/S1048953300000010 https://doi.org/10.1155/S1048953300000010 https://hdl.handle.net/2346/95705 |
op_doi |
https://doi.org/10.1155/S1048953300000010 |
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Journal of Applied Mathematics and Stochastic Analysis |
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13 |
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1 |
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1 |
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14 |
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1778145386734551040 |