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Quantizing for minimum distortion
Abstract
This paper discusses the problem of the minimization of the distortion of a signal by a quantizer when the number of output levels of the quantizer is fixed. The distortion is defined as the expected value of some function of the error between the input and the output of the quantizer. Equations are derived for the parameters of a quantizer with minimum distortion. The equations are not soluble without recourse to numerical methods, so an algorithm is developed to simplify their numerical solution. The case of an input signal with normally distributed amplitude and an expected squared error distortion measure is explicitly computed and values of the optimum quantizer parameters are tabulated. The optimization of a quantizer subject to the restriction that both input and output levels be equally spaced is also treated, and appropriate parameters are tabulated for the same case as above.
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Citations
Cited by
A theory for multiresolution signal decomposition: the wavelet representation
Mallat, S. G. (1989) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.192463 · Cited by 21,372
Kohonen, T. (1990) · Proceedings of the IEEE · doi:10.1109/5.58325 · Cited by 8,414
An Algorithm for Vector Quantizer Design
Linde, Y., Buzo, A., & Gray, R. (1980) · IEEE Transactions on Communications · doi:10.1109/tcom.1980.1094577 · Cited by 7,201
Zwanenburg, A., Vallières, M., Abdalah, M. A., Aerts, H. J. W. L., Andrearczyk, V., Apte, A., Ashrafinia, S., Bakas, S., Beukinga, R. J., Boellaard, R., et al. (2020) · Radiology · doi:10.1148/radiol.2020191145 · Cited by 4,177
Bakas, S., Akbari, H., Sotiras, A., Bilello, M., Rozycki, M., Kirby, J. S., Freymann, J. B., Farahani, K., & Davatzikos, C. (2017) · Scientific Data · doi:10.1038/sdata.2017.117 · Cited by 3,049
Metadata
- Authors
- Max, J.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1960-03
- Volume
- 6
- Issue
- 1
- Pages
- 7-12
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2109808436
- Cited by
- 2,038
- References
- 0
- FWCI
- 12.23
- Type
- journal article
- Language
- en
- Open access
- closed
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- Max, J. (1960). Quantizing for minimum distortion. IEEE Transactions on Information Theory. https://doi.org/10.1109/tit.1960.1057548
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