ICA based algorithms for computing optimal 1-D linear block transforms in variable high-rate source coding
The Karhunen–Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources. Furthermore, under the high-resolution quantization hypothesis, nearly everything is known about the performance of a transform coding system with...
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| Veröffentlicht in: | Signal processing Jg. 88; H. 2; S. 268 - 283 |
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| Abstract | The Karhunen–Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources. Furthermore, under the high-resolution quantization hypothesis, nearly everything is known about the performance of a transform coding system with entropy constrained scalar quantization and mean-square distortion. It is then straightforward to find a criterion that, when minimized, gives the optimal linear transform under the abovementioned conditions. However, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculus. In this paper, we present the abovementioned criterion as a contrast of independent component analysis modified by an additional term which is a penalty to non-orthogonality. Then we adapt the
icainf algorithm by Pham in order to compute the transform minimizing the criterion either with no constraint or with the orthogonality constraint. Finally, experimental results show that the transforms we introduced can (1) outperform the KLT on synthetic signals, (2) achieve slightly better PSNR for high-rates and better visual quality (preservation of lines and contours) for medium-to-low rates than the KLT and 2-D DCT on grayscale natural images. |
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| AbstractList | The Karhunen-Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources. Furthermore, under the high-resolution quantization hypothesis, nearly everything is known about the performance of a transform coding system with entropy constrained scalar quantization and mean-square distortion. It is then straightforward to find a criterion that, when minimized, gives the optimal linear transform under the abovementioned conditions. However, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculus. In this paper, we present the abovementioned criterion as a contrast of independent component analysis modified by an additional term which is a penalty to non-orthogonality. Then we adapt the icainf algorithm by Pham in order to compute the transform minimizing the criterion either with no constraint or with the orthogonality constraint. Finally, experimental results show that the transforms we introduced can (1) outperform the KLT on synthetic signals, (2) achieve slightly better PSNR for high-rates and better visual quality (preservation of lines and contours) for medium-to-low rates than the KLT and 2-D DCT on grayscale natural images. The Karhunen–Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources. Furthermore, under the high-resolution quantization hypothesis, nearly everything is known about the performance of a transform coding system with entropy constrained scalar quantization and mean-square distortion. It is then straightforward to find a criterion that, when minimized, gives the optimal linear transform under the abovementioned conditions. However, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculus. In this paper, we present the abovementioned criterion as a contrast of independent component analysis modified by an additional term which is a penalty to non-orthogonality. Then we adapt the icainf algorithm by Pham in order to compute the transform minimizing the criterion either with no constraint or with the orthogonality constraint. Finally, experimental results show that the transforms we introduced can (1) outperform the KLT on synthetic signals, (2) achieve slightly better PSNR for high-rates and better visual quality (preservation of lines and contours) for medium-to-low rates than the KLT and 2-D DCT on grayscale natural images. |
| Author | Pham, Dinh-Tuan Barret, Michel Narozny, Michel |
| Author_xml | – sequence: 1 givenname: Michel surname: Narozny fullname: Narozny, Michel email: Michel.Narozny@supelec.fr organization: SUPELEC, Information Multimodality & Signal Team, 2 rue É. Belin 57070 Metz, France – sequence: 2 givenname: Michel surname: Barret fullname: Barret, Michel email: Michel.Barret@supelec.fr organization: SUPELEC, Information Multimodality & Signal Team, 2 rue É. Belin 57070 Metz, France – sequence: 3 givenname: Dinh-Tuan surname: Pham fullname: Pham, Dinh-Tuan email: Dinh-Tuan.Pham@imag.fr organization: Jean Kuntzmann Laboratory, 51 rue des Mathématiques, BP 53, 38041 Grenoble Cedex 9, France |
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| Keywords | Non-Gaussian signals Image compression Transform coding Independent component analysis Performance evaluation High resolution Karhunen Loeve transformation Source coding Grey level image Image processing Data compression Entropy Orthogonality Algorithm Varying speed Image quality Image coding Signal quantization Gaussian signal Linear transformation Signal processing Optimal code Discrete cosine transforms Signal to noise ratio |
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| Snippet | The Karhunen–Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources.... The Karhunen-Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however, it is not optimal, in general, for non-Gaussian sources.... |
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| SubjectTerms | Applied sciences Coding, codes Computer Science Detection, estimation, filtering, equalization, prediction Engineering Sciences Exact sciences and technology Image compression Independent component analysis Information, signal and communications theory Mathematics Miscellaneous Non-Gaussian signals Optimization and Control Sampling, quantization Signal and communications theory Signal and Image Processing Signal processing Signal, noise Telecommunications and information theory Transform coding |
| Title | ICA based algorithms for computing optimal 1-D linear block transforms in variable high-rate source coding |
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