Extending the Quantum Entropy to Multidimensional Signal Processing

This paper treats different aspects of entropy measure in classical information theory and statistical quantum mechanics, it presents the possibility of extending the definition of Von Neumann entropy to image and array processing. In the first part, we generalize the quantum entropy using singular values of arbitrary rectangular matrices to measure the randomness and the quality of denoising operation, this new definition of entropy can be implemented to compare the performance analysis of filtering methods. In the second part, we apply the concept of pure state in quantum formalism to generalize the maximum entropy method for narrowband and farfield source localization problem. Several computer simulation results are illustrated to demonstrate the effectiveness of the proposed techniques.

Authors:

• Youssef Khmou
• Said Safi
• Miloud Frikel

Keywords:

• Von Neumann entropy
• Filtering
• array
• DoA
• Maximum Entropy Method.

References:

[1] Shannon, C.E., ”A mathematical theory of communication,” Bell System
Technical Journal, The , vol.27, no.3, pp.379,423, July 1948.
[2] Yue Wu, Yicong Zhou, George Saveriades, Sos Agaian, Joseph P. Noonan,
Premkumar Natarajan, Local Shannon entropy measure with statistical
tests for image randomness, Information Sciences, Volume 222, 10
February 2013, Pages 323-342.
[3] John von Neumann, Mathematische Grundlagen der Quantenmechanik,
Springer, 1995.
[4] Peter J. Schreier and Louis L. Scharf, Statistical Signal Processing of
Complex-Valued Data, Cambridge University Press, 2010.
[5] Pratt, W., ”Generalized Wiener Filtering Computation Techniques,”
Computers, IEEE Transactions on , vol.C-21, no.7, pp.636,641, July 1972.
[6] Zhizhang Chen, Gopal Gokeda and Yiqiang Yu, Introduction to
Direction-Of-Arrival Estimation, Artech House, 2010.
[7] Youssef Khmou, Said Safi and Miloud Frikel, Generalized Maximum
Entropy Method for Cosmic Source Localization, International Journal
of Mathematical, Computational, Statistical, Natural and Physical
Engineering, 2014.
[8] Sylvie Marcos, Alain Marsal, Messaoud Benidir, The propagator method
for source bearing estimation, Signal Processing, Volume 42, Issue 2,
March 1995, Pages 121-138.
[9] Ermolaev, V.T.; Gershman, A.B., ”Fast algorithm for minimum-norm
direction-of-arrival estimation,” Signal Processing, IEEE Transactions on
, vol.42, no.9, pp.2389,2394, Sep 1994.
[10] Bouri, M. , Bourennane, S.. ”High Resolution Methods Based On
Rank Revealing Triangular Factorizations ”. World Academy of Science,
Engineering and Technology, International Science Index 3, International
Journal of Mathematical, Computational, Statistical, Natural and Physical
Engineering (2007), 1(3), 190 - 193.