Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution

• Autorzy: Ewa Świercz
• Języki publikacji: EN

Abstrakty

EN

A new supervised classification algorithm of a heavily distorted pattern (shape) obtained from noisy observations of nonstationary signals is proposed in the paper. Based on the Gabor transform of 1-D non-stationary signals, 2-D shapes of signals are formulated and the classification formula is developed using the pattern matching idea, which is the simplest case of a pattern recognition task. In the pattern matching problem, where a set of known patterns creates predefined classes, classification relies on assigning the examined pattern to one of the classes. Classical formulation of a Bayes decision rule requires a priori knowledge about statistical features characterising each class, which are rarely known in practice. In the proposed algorithm, the necessity of the statistical approach is avoided, especially since the probability distribution of noise is unknown. In the algorithm, the concept of discriminant functions, represented by Frobenius inner products, is used. The classification rule relies on the choice of the class corresponding to the max discriminant function. Computer simulation results are given to demonstrate the effectiveness of the new classification algorithm. It is shown that the proposed approach is able to correctly classify signals which are embedded in noise with a very low SNR ratio. One of the goals here is to develop a pattern recognition algorithm as the best possible way to automatically make decisions. All simulations have been performed in Matlab. The proposed algorithm can be applied to non-stationary frequency modulated signal classification and non-stationary signal recognition.

Słowa kluczowe

EN

non-stationary signals; signal classification; pattern recognition; time-frequency transforms

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2010
• Tom: 20
• Numer: 1
• Strony: 135-147

Daty

wydano

2010

otrzymano

2008-07-29

poprawiono

2009-07-06

Twórcy

autor

Ewa Świercz

• Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45D, 15-351 Białystok, Poland

Bibliografia

• Auger F., Flandrin P., Goncalves P. and Lemoine O. (1996). Time-Frequency Toolbox for Matlab, CNRS, Rice University, Houston, TX, http://iut-saint-nazaire.univ-nantes.fr/˜{}auger/tftb.html.
• Basri R., Costa L., Geiger D. and Jacobs D. (1998). Determining the similarity of deformable shapes, Vision Research 38(15-16): 2365-2385.
• Basseville M. (1989). Distance measures for signal processing and pattern recognition, Signal Processing 35(3): 349-369.
• Belongie S., Malik J. and Puzicha J. (2002). Shape matching and object recognition using shape contexts, IEEE Transactions on Pattern Analysis and Machine Intelligence 24(4): 509-522.
• Bishop C. M. (2006). Pattern Recognition and Machine Learning (Information Science and Statistics), Springer Science + Business Media LLC, New York, NY.
• Breakenridge C. and Mesbah M. (2003). Minimum classification error using time-frequency analysis, Proceedings of the 3rd IEEE International Symposium on Signal Processing and Information Technology (ISSPIT 2003), Darmstad, Germany, pp. 717-720.
• Colas M. and Gelle G. (2004). A multitime-frequency approach for detection and classification of neighboring instantaneous frequency laws in a noisy environment, Signal Processing Letters 11(2): 71-74.
• Davy M. and Doncarli C. (1998). Optimal kernels of timefrequency representations for signal classification, Proceedings of the International Symposium Time-Frequency and Time-Scale, Pittsburgh, PA, USA, pp. 581-584.
• Demirci M. F., van Leuken R. H. and Veltkamp R. C. (2007). Shape indexing through laplacian spectra, Proceedings of the International Conference on Image Analysis and Processing Workshops (ICIAPW 2007), Modena, Italy, pp. 21-26.
• Doncarli C., Davy M. and Boudreaux-Bartels F. (2001). Improved optimization of time-frequency-based signal classifiers, IEEE Signal Processing Letters 8(2): 52-57.
• Duda R. O., Hart P. E. and Stork D. G. (2001). Pattern Classification, 2nd Edition, John Wiley & Sons, Inc., New York, NY.
• Flandrin P. (1988). A time-frequency formulation of optimal detection, IEEE Transactions on Acoustics, Speech and Signal Processing 36(9): 1337-1384.
• Fry D. (1993). Shape Recognition Using Metrics on the Space of Shapes, Ph.D. thesis, Harvard University, Cambridge, MA.
• Fukunaga K. (1990). Introduction to Statistical Pattern Recognition, 2nd Edition, Academic Press, London.
• Gdalyahu Y. and Weinshall D. (1999). Flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes, IEEE Transactions on Pattern Analysis and Machine Intelligence 21(12): 1312-1328.
• Gillespie B. and Atlas L. (2001). Optimizing time-frequency kernels for classification, IEEE Transactions on Signal Processing 49(3): 485-496.
• Grigorescu S. E., Petkov N. and Kruizinga P. (2002). Comparison of texture features based on Gabor filters, IEEE Transactions on Image Processing 11(10): 1160-1167.
• Gröchenig K. (2001). Foundations of Time-Frequency Analysis, Birkhäuser, Boston, MA, pp. 83-142.
• Hagedoorn M. and Veltkamp R. C. (1999). Reliable and efficient pattern matching using an affine invariant metric, Journal of Computer Vision 31(2/3): 203-225.
• Heitz C. (1995). Optimum time-frequency representations for the classification and detection of signals, Applied Signal Processing 2(3): 124-143.
• Huang Y., Chan K. L. and Zhang Z. (2003). Texture classification by multi-model feature integration using Bayesian networks, Pattern Recognition Letters 24(1-3): 393-401.
• Jain A. K., Duin R. P. W. and Mao J. (2000). Statistical pattern recognition: A review, IEEE Transactions on Pattern Analysis and Machine Intelligence 22(1): 4-7.
• Kyrki V., Kamarainen J.-K. and Klviinen H. (2004). Simple Gabor feature space for invariant object recognition, Pattern Recognition Letters 25(3): 311-318.
• Latecki L. J. and Lakamper R. (2000). Shape similarity measure based on correspondence of visual parts, IEEE Transactions on Pattern Analysis and Machine Intelligence 22(10): 1185-1190.
• Li S. and Shawe-Taylor S. (2005). Comparison and fusion of multiresolution features for texture classification, Pattern Recognition Letters 26(5): 633-638.
• Liu H. and Srinath M. (1990). Partial shape classification using contour matching in distance transforms, IEEE Transactions on Pattern Analysis and Machine Intelligence 12(2): 1072-1079.
• Manay S., Cremers D., Hong B.-W., Yezzi A. J. Jr. and Soatto S. (2006). Integral invariants for shape matching, IEEE Transactions on Pattern Analysis and Machine Intelligence 28(10): 1602-1618.
• McLachlan G. J. (1992). Discriminant Analysis and Statistical Pattern Recognition, Wiley Series in Probability and Statistics, John Wiley & Sons, Inc., New York, NY.
• Petrakis E. G. M., Diplaros A. and Milios E. (2002). Matching and retrieval of distorted and occluded shapes using dynamic programming, IEEE Transactions on Pattern Analysis and Machine Intelligence 24(11): 1501-1516.
• Qian S. and Chen D. (1993). Discrete Gabor Transform, IEEE Transactions on Signal Processing 41(7): 2429-2438.
• Richard C. and Lengell R. (1999). Data driven design and complexity control of time frequency detectors, Signal Processing 77(1): 37-48.
• Santini S. and Jain R. (1999). Similarity measures, IEEE Transactions on Pattern Analysis and Machine Intelligence 21(9): 871-883.
• Sebe N. and Lew M. S. (2002). Maximum likelihood shape matching, Proceedings of the 5th Asian Conference on Computer Vision (ACCV2002), Melbourne, Australia, Vol. 1, pp. 713-718.
• Sejdic E., Djurovic I. and Jiang J. (2009). Time-frequency feature representation using energy concentration: An overview of recent advances, Digital Signal Processing 19(1): 153-183.
• Sondergaard P. (2006). Time-Frequency Toolbox for Matlab, Technical University of Denmark, Lyngby, http://www2.mat.dtu.dk/people/P.Soendergaard/toolbox/.
• Tai C.-F. (2007). Image mining by spectral features: A case study of scenery image classification, Expert Systems with Applications 32(1): 135-142.
• Umeyama S. (1993). Parameterized point pattern matching and its application to recognition of object families, IEEE Transactions on Pattern Analysis and Machine Intelligence 15(2): 136-144.
• Veltkamp R. C. (2001). Shape matching: Similarity measures and algorithms, Technical Report UU-CS-2001-03, Utrecht University, Utrecht.
• Vincent I., Doncarli C. and Carpentier E. L. (1994). Nonstationary signals classification using time-frequency distributions, Proceedings of the International Symposium on Time-Frequency and Time Scale, Paris, France, pp. 233-236.
• Werther T., Eldar Y. C. and Subanna N. K. (2005). Dual Gabor frames: Theory and computational aspects, IEEE Transactions on Signal Processing 53(11): 4147-4158.
• Xie J., Hengb P.-A. and Shah M. (2008). Shape matching and modeling using skeletal context, Pattern Recognition 41(5): 1773-1784.
• Younes L. (1999). Optimal matching between shapes via elastic deformations, Image and Vision Computing 17(5-7): 381-389.
• Zhang D. and Lu G. (2003). A comparative study of curvature scale space and Fourier descriptors for shape-based image retrieval, Journal of Visual Communication and Image Representation 14(1): 41-60.
• Zhang D. and Lu G. (2004). Review of shape representation and description techniques, Pattern Recognition 37(1): 1-19.

Identyfikatory

DOI

10.2478/v10006-010-0010-x