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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Vydáno v:Signal processing Ročník 88; číslo 2; s. 268 - 283
Hlavní autoři: Narozny, Michel, Barret, Michel, Pham, Dinh-Tuan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.02.2008
Elsevier Science
Elsevier
Témata:
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
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
ISSN:0165-1684, 1872-7557
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Popis
Shrnutí: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.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2007.07.017