**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30184

##### Learning an Overcomplete Dictionary using a Cauchy Mixture Model for Sparse Decay

**Authors:**
E. S. Gower,
M. O. J. Hawksford

**Abstract:**

**Keywords:**
expectation-maximization,
Pitman estimator,
sparsedecomposition

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1075030

**References:**

[1] M. S. Lewicki and T. J. Sejnowski, "Learning Overcomplete Representations, " Neural Computations, vol. 12, No. 2, pp. 337-365, February 2000.

[2] M. Zhong, H. Tang, H. Cheng and Y. Tang, "An EM Algorithm for Learning Sparse and Overcomplete Representations, " Neurocomputing, vol. 57, pp. 467-476, 2004.

[3] M. Aharon, M. Elad and A. Bruckstein, "K-SVD: An algorithm for Designing Overcomplete Dictionaries for Sparse Representations," IEEE Transactions on Signal Processing, vol. 54, No. 11, November 2006.

[4] K. Kreutz-Delgado, J. F. Murray, B. D. Rao, K. Egan, T. Lee and T. J. Sejnowski, "Dictionary Learning Algorithms for Sparse Representations, " eural Computations, vol. 15, No. 2, pp. 349-396, 2003.

[5] K. Egan, S. O. Aase and J. H. Hakon-Husoy, "Method of Optimal Directions for Frame Design, "in IEEE International Conference of Acoustic, Speech and Signal Processing, Vol. 5, pp. 2443-2446, 1999.

[6] I. T. Jollife, Principal Component Analysis, Series: Springer Series in Statistics, 2nd Edition, .

[7] P. Common, "Independent Component Analysis: A new Concept?, " Signal Processing, vol. 36, pp. 287-314, 1994.

[8] G. Marsaglia, "Ratios of Normal Variables, " Journal of Statistical Software, vol. 16, No. 4, May 2006.

[9] W. Feller, An Introduction to Probability Theory and Applications, 2nd Edition, New York: Wiley, pp. 229-235, 1968.

[10] P. G. Hoel, Introduction to Mathematical Statistics, 3rd Edition, New York: Wiley, pp. 57-62, 1962.

[11] J. W. Harris and H. Stoker, "Maximum Likelihood Method, " in Handbook of Mathematics and Computational Science, New York: Springer-Verlag, pp. 824-835, 1998.

[12] A. Koutrouvelis, "Estimation of the Location and Scale of the Cauchy Distribution using the Empirical Characteristic Function, " Biometrica, Vol. 69, pp. 205-213, 1982.

[13] F. Nagy, "Parameter Estimation of the Cauchy Distribution in Information Theory Approach, "Journal of Universal Computer Science, Vol. 12, No. 9, pp. 1332-1344, May 2006.

[14] G. B. Freue, "The Pitman Estimator of the Cauchy Location Parameter, " Journal of Statistical Planning and Inference, vol. 137, pp. 1900-1913, May 2006.

[15] K. M. Hanson and D. R. Wolf, "Estimators for the Cauchy Distribution, " In Maximum Entropy and Bayesian Methods, pp. 255-263, 1996.

[16] C. Jutten, G. H. Mohimani and M. B. Zadeh, "Fast Sparse Representations based on the l0 Norm, " In Pro. ICA-07, London, UK, 2007.

[17] G. H. Mohimani, M. B. Zaden and C. Jutten, "Complex Valued Sparse Representations based on Smoothed l0 Norm, " In ICASSP-08, 2008.

[18] S. S. Chen, D. L. Donoho and M. A. Saunders, "Atomic Decomposition by Basis Pursuit, " SIAM Journal of Computing, Vol. 20, No. 1, pp. 33- 61, 1999.

[19] S. G. Mallat and Z. Zhang, "Matching Pursuit with Time-Frequency Dictionaries, " IEEE Transactions on Signal Processing, pp. 3397-3415, December 1993.

[20] I. F. Gorodnitsky and B. D. Rao, "Sparse Signal Reconstruction from Limited Data using FOCUSS: A Re-weighted Minimum Norm Algorithm, " IEEE Transactions on Signal Processing, Vol. 45, No. 3, March 1997.

[21] J. E. Marsden and J. M. Hoffman, Basic Complex Analysis, 3rd Edition, W. H. Freeman, 1998, ISBN: 978-0716728771.