K-SVD dictionary learning using a fast OMP with applications

K-SVD method has recently been introduced to learn a specific dictionary matrix that best fits a set of training data vectors. K-SVD is flexible in that any preferred pursuit method of sparse coding can be used to represent the data. In this paper, we show how K-SVD method can be used in conjunction with a fast orthogonal matching pursuit implemented using orthogonal projection updating. Geometric interpretation of this learning is also presented. The method was then applied to underwater target detection problem using a dual-channel sonar imagery data.

[1]  Joseph F. Murray,et al.  Dictionary Learning Algorithms for Sparse Representation , 2003, Neural Computation.

[2]  T. Kailath,et al.  Fast, recursive-least-squares transversal filters for adaptive filtering , 1984 .

[3]  Baoxin Li,et al.  Discriminative K-SVD for dictionary learning in face recognition , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[4]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[5]  S. T. Alexander,et al.  Adaptive Signal Processing: Theory and Applications , 1986 .

[6]  Zhifeng Zhang,et al.  Adaptive time-frequency decompositions , 1994 .

[7]  D. Brown,et al.  Results from a Small Synthetic Aperture Sonar , 2006, OCEANS 2006.

[8]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[9]  Richard Bamler,et al.  A comparison of range-Doppler and wavenumber domain SAR focusing algorithms , 1992, IEEE Trans. Geosci. Remote. Sens..

[10]  David G. Stork,et al.  Pattern Classification , 1973 .

[11]  Shigeo Abe DrEng Pattern Classification , 2001, Springer London.

[12]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[13]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[14]  Yvan Petillot,et al.  Automated approach to classification of mine-like objects in sidescan sonar using highlight and shadow information , 2004 .

[15]  Mahmood R. Azimi-Sadjadi,et al.  Detection of Spatially Correlated Time Series From a Network of Sensor Arrays , 2014, IEEE Transactions on Signal Processing.

[16]  B.D. Rao,et al.  Comparison of basis selection methods , 1996, Conference Record of The Thirtieth Asilomar Conference on Signals, Systems and Computers.

[17]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..