General uncertainty relations and sparse signal recovery
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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Konstanz
Hartung-Gorre
2011
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| Ausgabe: | 1. ed. |
| Schriftenreihe: | Series in communication theory
8 |
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| 245 | 1 | 0 | |a General uncertainty relations and sparse signal recovery |c Patrick Rudolf Emil Kuppinger |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Konstanz |b Hartung-Gorre |c 2011 | |
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| 490 | 1 | |a Series in communication theory |v 8 | |
| 502 | |a Zugl.: Zürich, Techn. Hochsch., Diss., 2011 | ||
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Datensatz im Suchindex
| _version_ | 1819684983815536640 |
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| adam_text | IMAGE 1
CONTENTS
ACKNOWLEDGMENTS XIII
1. INTRODUCTION 1
1.1. UNCERTAINTY RELATIONS AND SPARSITY THRESHOLDS . . .. 2
1.2. OUTLINE AND CONTRIBUTIONS 6
I PAIRS OF DICTIONARIES 11
2. UNCERTAINTY RELATIONS FOR PAIRS OF DICTIONARIES 13
2.1. COHERENCE MEASURES 15
2.2. BRIEF REVIEW OF KNOWN UNCERTAINTY RELATIONS 17 2.3. A GENERAL
UNCERTAINTY RELATION 18
2.4. TIGHTNESS OF THE UNCERTAINTY RELATION FOR GENERAL DIC- TIONARIES 20
2.5. TECHNICAL RESULTS 21
2.5.1. PROOF OF THEOREM 2.1 21
3. RECOVERY GUARANTEES FOR CONCATENATIONS OF DICTIONARIES 25 3.1.
RECOVERY METHODS 28
3.1.1. THE (P0) PROBLEM 28
3.1.2. BASIS PURSUIT 29
3.1.3. (ORTHOGONAL) MATCHING PURSUIT 29
3.2. DETERMINISTIC RECOVERY GUARANTEES 31
3.2.1. BRIEF REVIEW OF RELEVANT PREVIOUS RESULTS . . . 31
XV
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010783289
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
3.2.2. UNIQUENESS OF (PO) 33
3.2.3. RECOVERY GUARANTEES FOR BP AND OMP 37
3.2.4. OBSERVATIONS 40
3.3. PROBABILISTIC RECOVERY GUARANTEES 41
3.3.1. BRIEF REVIEW OF RELEVANT PREVIOUS RESULTS . . . 41 3.3.2. ROBUST
SPARSITY THRESHOLDS 43
3.3.3. INTERPRETATION OF THE RESULTS 45
3.4. TECHNICAL RESULTS 49
3.4.1. PROOF OF THEOREM 3.2 49
3.4.2. PROOF OF THEOREM 3.3 52
3.4.3. PROOF OF COROLLARY 3.4 56
3.4.4. PROOF OF LEMMA 3.7 58
4. RECOVERY OF SPARSELY CORRUPTED SIGNALS 63
4.1. BRIEF REVIEW OF PREVIOUS RESULTS 66
4.1.1. RECOVERY IN THE PRESENCE OF UNSTRUCTURED NOISE 66 4.1.2. RECOVERY
IN THE PRESENCE OF STRUCTURED NOISE . 67 4.2. DETERMINISTIC RECOVERY
GUARANTEES 69
4.2.1. CASE I: KNOWLEDGE OF X AND E 69
4.2.2. CASE II: EITHER X OR S IS KNOWN 71
4.2.3. CASE III: CARDINALITY OF X OR S KNOWN 76
4.2.4. CASE IV: NO KNOWLEDGE ABOUT THE SUPPORT SETS 77 4.3. OBSERVATIONS
78
4.3.1. TIGHTNESS OF THE RECOVERY GUARANTEES IN THE FOURIER-IDENTITY CASE
78
4.3.2. FACTOR OF TWO IN THE RECOVERY GUARANTEES . .. 81 4.3.3. TRADEOFF
BETWEEN SIGNAL AND ERROR SPARSITY . . 82 4.4. NUMERICAL RESULTS 85
4.4.1. IMPACT OF SUPPORT-SET KNOWLEDGE ON THE RE- COVERY THRESHOLDS 85
4.4.2. INPAINTING EXAMPLE 89
4.5. TECHNICAL RESULTS 91
4.5.1. PROOF OF THEOREM 4.1 91
4.5.2. PROOF OF THEOREM 4.2 92
4.5.3. PROOF OF THEOREM 4.3 94
XVI
IMAGE 3
CONTENTS
4.5.4. PROOF OF THEOREM 4.5 98
II BLOCK-SPARSE SIGNALS 103
5. UNCERTAINTY RELATIONS FOR BLOCK-SPARSE SIGNALS 105 5.1. COHERENCE
MEASURES FOR THE BLOCK-SPARSE CASE . . .. 107 5.2. UNCERTAINTY RELATION
112
5.3. OBSERVATIONS 114
6. RECOVERY GUARANTEES FOR BLOCK-SPARSE SIGNALS 117 6.1. RECOVERY
METHODS 118
6.1.1. THE BLOCK-(PO) PROBLEM 118
6.1.2. 2 /^I-OPTIMIZATION PROGRAM 119
6.1.3. BLOCK (ORTHOGONAL) MATCHING PURSUIT 120 6.2. BRIEF REVIEW OF
PREVIOUS RESULTS 121
6.3. DETERMINISTIC RECOVERY GUARANTEES 122
6.3.1. UNIQUENESS OF BLOCK-(PO) 123
6.3.2. RECOVERY GUARANTEES FOR L-OPT AND BOMP . .. 123 6.3.3. RECOVERY
GUARANTEES FOR BMP 125
6.3.4. OBSERVATIONS 125
6.3.5. NUMERICAL RESULTS 128
6.4. TECHNICAL RESULTS 131
6.4.1. PROOF OF THEOREM 6.2 134
6.4.2. PROOF OF THEOREM 6.3 FOR BOMP 135
6.4.3. PROOF OF THEOREM 6.3 FOR L-OPT 136
6.4.4. PROOF OF THEOREM 6.4 138
6.4.5. PROOF OF THEOREM 6.5 140
7. CONCLUSION 143
7.1. IMPLICATIONS FOR PRACTICAL APPLICATIONS 144
7.2. OPEN PROBLEMS 145
A. ADDITIONAL TECHNICAL RESULTS 147
A.I. PART I 147
XVN
IMAGE 4
CONTENTS
A.1.1. THE SPARSITY THRESHOLD IN THEOREM 3.2 IM- PROVES ON THE THRESHOLD
IN (3.7) 147
A.1.2. THE SPARSITY THRESHOLD IN COROLLARY 3.4 IM- PROVES ON THE
THRESHOLD IN (3.7) 148
A.1.3. TROPP S (MO) AND (ML) MODEL 149
A.2. PART II 151
A.2.1. PROOF OF LEMMA 6.6 151
A.2.2. PROOF OF LEMMA 6.7 152
A.2.3. PROOF OF LEMMA 6.8 153
B. NOTATION 155
B.I. MISCELLANEOUS 155
B.2. LINEAR ALGEBRA 156
B.3. PROBABILITY AND STATISTICS 157
B.4. PAIRS OF DICTIONARIES 158
B.5. BLOCK-SPARSE SIGNALS 159
C. ACRONYMS AND ABBREVIATIONS 161
REFERENCES 163
XVM
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| discipline | Allgemeines Informatik |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV040491517 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T02:51:22Z |
| institution | BVB |
| isbn | 9783866283855 3866283857 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025338500 |
| oclc_num | 723484666 |
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| owner | DE-473 DE-BY-UBG |
| owner_facet | DE-473 DE-BY-UBG |
| physical | XVIII, 172 S. graph. Darst. 21 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Hartung-Gorre |
| record_format | marc |
| series | Series in communication theory |
| series2 | Series in communication theory |
| spellingShingle | Kuppinger, Patrick Rudolf Emil General uncertainty relations and sparse signal recovery Series in communication theory Schwach besetzte Matrix (DE-588)4056053-3 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Abtasttheorem (DE-588)4258507-7 gnd Signalregenerierung (DE-588)4181274-8 gnd |
| subject_GND | (DE-588)4056053-3 (DE-588)4035826-4 (DE-588)4258507-7 (DE-588)4181274-8 (DE-588)4113937-9 |
| title | General uncertainty relations and sparse signal recovery |
| title_auth | General uncertainty relations and sparse signal recovery |
| title_exact_search | General uncertainty relations and sparse signal recovery |
| title_full | General uncertainty relations and sparse signal recovery Patrick Rudolf Emil Kuppinger |
| title_fullStr | General uncertainty relations and sparse signal recovery Patrick Rudolf Emil Kuppinger |
| title_full_unstemmed | General uncertainty relations and sparse signal recovery Patrick Rudolf Emil Kuppinger |
| title_short | General uncertainty relations and sparse signal recovery |
| title_sort | general uncertainty relations and sparse signal recovery |
| topic | Schwach besetzte Matrix (DE-588)4056053-3 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Abtasttheorem (DE-588)4258507-7 gnd Signalregenerierung (DE-588)4181274-8 gnd |
| topic_facet | Schwach besetzte Matrix Lineares Gleichungssystem Abtasttheorem Signalregenerierung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025338500&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035738068 |
| work_keys_str_mv | AT kuppingerpatrickrudolfemil generaluncertaintyrelationsandsparsesignalrecovery |