Measuring time-Frequency information content using the Rényi entropies
By Richard Baraniuk, Patrick Flandrin, Augustus J. E. M. Janssen, Olivier J. J. Michel. IEEE Transactions on Information Theory, 2001
483 citations recorded by the source corpus.
The generalized entropies of Renyi inspire new measures for estimating signal information and complexity in the time-frequency plane. When applied to a time-frequency representation (TFR) from Cohen's class or the affine class, the Renyi entropies conform closely to the notion of complexity that we use when visually inspecting time-frequency images. These measures possess several additional interesting and useful properties, such as accounting and cross-component and transformation invariances, that make them natural for time-frequency analysis. This paper comprises a detailed study of the properties and several potential applications of the Renyi entropies, with emphasis on the mathematical foundations for quadratic TFRs. In particular, for the Wigner distribution, we establish that there exist signals for which the measures are not well defined.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing
View Paper: https://www.semanticscholar.org/paper/2141d4ce1bd5ed6837c1822edbdc343c1f29bd5c
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Citations in the corpus
- Acoustic classification of Australian anurans based on hybrid spectral-entropy approach (2011, methodology): “Rényi entropy have been used in communication and coding theory [14], data mining, detection, segmentation, classification [15], characterization of signals and sequences [16], signal processing [17], image matching and registration [15].”
- Time-frequency feature representation using energy concentration: An overview of recent advances (2009, background): “A detailed study of the properties and some potential applications of the Rényi TF information measures, with emphasis on the mathematical foundations for quadratic TFRs can be found in [121].”
- On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles (2006, background): “statistical mechanics, physics of turbulence, cosmology, see [10,11,12] and references therein), but in various other areas such as in signal processing (time scale analysis, decision problems, machine learning, see [4,13,14,15] and references therein), or image processing (image matching, image reg”