Quantization and erasures in frame representations
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2007
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| Online Access: | http://hdl.handle.net/1721.1/35288 |
| _version_ | 1826207568485154816 |
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| author | Boufounos, Petros T., 1977- |
| author2 | Alan V. Oppenheimer. |
| author_facet | Alan V. Oppenheimer. Boufounos, Petros T., 1977- |
| author_sort | Boufounos, Petros T., 1977- |
| collection | MIT |
| description | Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006. |
| first_indexed | 2024-09-23T13:51:35Z |
| format | Thesis |
| id | mit-1721.1/35288 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:51:35Z |
| publishDate | 2007 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/352882019-04-12T09:21:37Z Quantization and erasures in frame representations Boufounos, Petros T., 1977- Alan V. Oppenheimer. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 123-126). Frame representations, which correspond to overcomplete generalizations to basis expansions, are often used in signal processing to provide robustness to errors. In this thesis robustness is provided through the use of projections to compensate for errors in the representation coefficients, with specific focus on quantization and erasure errors. The projections are implemented by modifying the unaffected coefficients using an additive term, which is linear in the error. This low-complexity implementation only assumes linear reconstruction using a pre-determined synthesis frame, and makes no assumption on how the representation coefficients are generated. In the context of quantization, the limits of scalar quantization of frame representations are first examined, assuming the analysis is using inner products with the frame vectors. Bounds on the error and the bit-efficiency are derived, demonstrating that scalar quantization of the coefficients is suboptimal. As an alternative to scalar quantization, a generalization of Sigma-Delta noise shaping to arbitrary frame representations is developed by reformulating noise shaping as a sequence of compensations for the quantization error using projections. (cont.) The total error is quantified using both the additive noise model of quantization, and a deterministic upper bound based on the triangle inequality. It is thus shown that the average and the worst-case error is reduced compared to scalar quantization of the coefficients. The projection principle is also used to provide robustness to erasures. Specifically, the case of a transmitter that is aware of the erasure occurrence is considered, which compensates for the erasure error by projecting it to the subsequent frame vectors. It is further demonstrated that the transmitter can be split to a transmitter/receiver combination that performs the same compensation, but in which only the receiver is aware of the erasure occurrence. Furthermore, an algorithm to puncture dense representations in order to produce sparse approximate ones is introduced. In this algorithm the error due to the puncturing is also projected to the span of the remaining coefficients. The algorithm can be combined with quantization to produce quantized sparse representations approximating the original dense representation. by Petros T. Boufounos. Sc.D. 2007-01-10T15:34:41Z 2007-01-10T15:34:41Z 2006 2006 Thesis http://hdl.handle.net/1721.1/35288 72707891 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 126 p. 883301 bytes 895053 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science. Boufounos, Petros T., 1977- Quantization and erasures in frame representations |
| title | Quantization and erasures in frame representations |
| title_full | Quantization and erasures in frame representations |
| title_fullStr | Quantization and erasures in frame representations |
| title_full_unstemmed | Quantization and erasures in frame representations |
| title_short | Quantization and erasures in frame representations |
| title_sort | quantization and erasures in frame representations |
| topic | Electrical Engineering and Computer Science. |
| url | http://hdl.handle.net/1721.1/35288 |
| work_keys_str_mv | AT boufounospetrost1977 quantizationanderasuresinframerepresentations |