Multi-Dimensional Sparse Models
Traditional synthesis/analysis sparse representation models signals in a one dimensional (1D) way, in which a multidimensional (MD) signal is converted into a 1D vector. 1D modeling cannot sufficiently handle MD signals of high dimensionality in limited computational resources and memory usage, as b...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 40(2018), 1 vom: 26. Jan., Seite 163-178 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , , , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2018
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | Traditional synthesis/analysis sparse representation models signals in a one dimensional (1D) way, in which a multidimensional (MD) signal is converted into a 1D vector. 1D modeling cannot sufficiently handle MD signals of high dimensionality in limited computational resources and memory usage, as breaking the data structure and inherently ignores the diversity of MD signals (tensors). We utilize the multilinearity of tensors to establish the redundant basis of the space of multi linear maps with the sparsity constraint, and further propose MD synthesis/analysis sparse models to effectively and efficiently represent MD signals in their original form. The dimensional features of MD signals are captured by a series of dictionaries simultaneously and collaboratively. The corresponding dictionary learning algorithms and unified MD signal restoration formulations are proposed. The effectiveness of the proposed models and dictionary learning algorithms is demonstrated through experiments on MD signals denoising, image super-resolution and texture classification. Experiments show that the proposed MD models outperform state-of-the-art 1D models in terms of signal representation quality, computational overhead, and memory storage. Moreover, our proposed MD sparse models generalize the 1D sparse models and are flexible and adaptive to both homogeneous and inhomogeneous properties of MD signals |
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| Beschreibung: | Date Completed 20.12.2018 Date Revised 20.12.2018 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2017.2663423 |