Minimax Theory of Image Reconstruction:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1993
|
| Schriftenreihe: | Lecture Notes in Statistics
82 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | There exists a large variety of image reconstruction methods proposed by different authors (see e. g. Pratt (1978), Rosenfeld and Kak (1982), Marr (1982)). Selection of an appropriate method for a specific problem in image analysis has been always considered as an art. How to find the image reconstruction method which is optimal in some sense? In this book we give an answer to this question using the asymptotic minimax approach in the spirit of Ibragimov and Khasminskii (1980a,b, 1981, 1982), Bretagnolle and Huber (1979), Stone (1980, 1982). We assume that the image belongs to a certain functional class and we find the image estimators that achieve the best order of accuracy for the worst images in the class. This concept of optimality is rather rough since only the order of accuracy is optimized. However, it is useful for comparing various image reconstruction methods. For example, we show that some popular methods such as simple linewise processing and linear estimation are not optimal for images with sharp edges. Note that discontinuity of images is an important specific feature appearing in most practical situations where one has to distinguish between the "image domain" and the "background" . The approach of this book is based on generalization of nonparametric regression and nonparametric change-point techniques. We discuss these two basic problems in Chapter 1. Chapter 2 is devoted to minimax lower bounds for arbitrary estimators in general statistical models |
| Beschreibung: | 1 Online-Ressource (XII, 258p) |
| ISBN: | 9781461227120 9780387940281 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4612-2712-0 |
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| 245 | 1 | 0 | |a Minimax Theory of Image Reconstruction |c by A. P. Korostelev, A. B. Tsybakov |
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| 500 | |a There exists a large variety of image reconstruction methods proposed by different authors (see e. g. Pratt (1978), Rosenfeld and Kak (1982), Marr (1982)). Selection of an appropriate method for a specific problem in image analysis has been always considered as an art. How to find the image reconstruction method which is optimal in some sense? In this book we give an answer to this question using the asymptotic minimax approach in the spirit of Ibragimov and Khasminskii (1980a,b, 1981, 1982), Bretagnolle and Huber (1979), Stone (1980, 1982). We assume that the image belongs to a certain functional class and we find the image estimators that achieve the best order of accuracy for the worst images in the class. This concept of optimality is rather rough since only the order of accuracy is optimized. However, it is useful for comparing various image reconstruction methods. For example, we show that some popular methods such as simple linewise processing and linear estimation are not optimal for images with sharp edges. Note that discontinuity of images is an important specific feature appearing in most practical situations where one has to distinguish between the "image domain" and the "background" . The approach of this book is based on generalization of nonparametric regression and nonparametric change-point techniques. We discuss these two basic problems in Chapter 1. Chapter 2 is devoted to minimax lower bounds for arbitrary estimators in general statistical models | ||
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| isbn | 9781461227120 9780387940281 |
| issn | 0930-0325 |
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| spelling | Korostelev, A. P. Verfasser aut Minimax Theory of Image Reconstruction by A. P. Korostelev, A. B. Tsybakov New York, NY Springer New York 1993 1 Online-Ressource (XII, 258p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 82 0930-0325 There exists a large variety of image reconstruction methods proposed by different authors (see e. g. Pratt (1978), Rosenfeld and Kak (1982), Marr (1982)). Selection of an appropriate method for a specific problem in image analysis has been always considered as an art. How to find the image reconstruction method which is optimal in some sense? In this book we give an answer to this question using the asymptotic minimax approach in the spirit of Ibragimov and Khasminskii (1980a,b, 1981, 1982), Bretagnolle and Huber (1979), Stone (1980, 1982). We assume that the image belongs to a certain functional class and we find the image estimators that achieve the best order of accuracy for the worst images in the class. This concept of optimality is rather rough since only the order of accuracy is optimized. However, it is useful for comparing various image reconstruction methods. For example, we show that some popular methods such as simple linewise processing and linear estimation are not optimal for images with sharp edges. Note that discontinuity of images is an important specific feature appearing in most practical situations where one has to distinguish between the "image domain" and the "background" . The approach of this book is based on generalization of nonparametric regression and nonparametric change-point techniques. We discuss these two basic problems in Chapter 1. Chapter 2 is devoted to minimax lower bounds for arbitrary estimators in general statistical models Statistics Statistics, general Statistik Minimum-Maximum-Prinzip (DE-588)4170060-0 gnd rswk-swf Nichtparametrische Schätzung (DE-588)4203980-0 gnd rswk-swf Bildrekonstruktion (DE-588)4145435-2 gnd rswk-swf Bildrekonstruktion (DE-588)4145435-2 s Nichtparametrische Schätzung (DE-588)4203980-0 s Minimum-Maximum-Prinzip (DE-588)4170060-0 s 1\p DE-604 Tsybakov, A. B. Sonstige oth https://doi.org/10.1007/978-1-4612-2712-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Korostelev, A. P. Minimax Theory of Image Reconstruction Statistics Statistics, general Statistik Minimum-Maximum-Prinzip (DE-588)4170060-0 gnd Nichtparametrische Schätzung (DE-588)4203980-0 gnd Bildrekonstruktion (DE-588)4145435-2 gnd |
| subject_GND | (DE-588)4170060-0 (DE-588)4203980-0 (DE-588)4145435-2 |
| title | Minimax Theory of Image Reconstruction |
| title_auth | Minimax Theory of Image Reconstruction |
| title_exact_search | Minimax Theory of Image Reconstruction |
| title_full | Minimax Theory of Image Reconstruction by A. P. Korostelev, A. B. Tsybakov |
| title_fullStr | Minimax Theory of Image Reconstruction by A. P. Korostelev, A. B. Tsybakov |
| title_full_unstemmed | Minimax Theory of Image Reconstruction by A. P. Korostelev, A. B. Tsybakov |
| title_short | Minimax Theory of Image Reconstruction |
| title_sort | minimax theory of image reconstruction |
| topic | Statistics Statistics, general Statistik Minimum-Maximum-Prinzip (DE-588)4170060-0 gnd Nichtparametrische Schätzung (DE-588)4203980-0 gnd Bildrekonstruktion (DE-588)4145435-2 gnd |
| topic_facet | Statistics Statistics, general Statistik Minimum-Maximum-Prinzip Nichtparametrische Schätzung Bildrekonstruktion |
| url | https://doi.org/10.1007/978-1-4612-2712-0 |
| work_keys_str_mv | AT korostelevap minimaxtheoryofimagereconstruction AT tsybakovab minimaxtheoryofimagereconstruction |