Sparse Approximation by Matching Pursuit Using Shift-Invariant Dictionary

Sparse approximation of signals using often redundant and learned data dependent dictionaries has been successfully used in many applications in signal and image processing the last couple of decades. Finding the optimal sparse approximation is in general an NP complete problem and many suboptimal solutions have been proposed: greedy methods like Matching Pursuit (MP) and relaxation methods like Lasso. Algorithms developed for special dictionary structures can often greatly improve the speed, and sometimes the quality, of sparse approximation.

[1]  Kjersti Engan,et al.  The flexible signature dictionary , 2015, 2015 23rd European Signal Processing Conference (EUSIPCO).

[2]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[3]  Kjersti Engan,et al.  Recursive Least Squares Dictionary Learning Algorithm , 2010, IEEE Transactions on Signal Processing.

[4]  Guillermo Sapiro,et al.  Online dictionary learning for sparse coding , 2009, ICML '09.

[5]  Jean Ponce,et al.  Sparse Modeling for Image and Vision Processing , 2014, Found. Trends Comput. Graph. Vis..

[6]  Shogo Muramatsu,et al.  Structured dictionary learning with 2-D non-separable oversampled lapped transform , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[7]  Zhifeng Zhang,et al.  Adaptive Nonlinear Approximations , 1994 .

[8]  B. Rao,et al.  Forward sequential algorithms for best basis selection , 1999 .

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

[10]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

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

[12]  John Hakon Husoy,et al.  Partial search vector selection for sparse signal representation , 2008 .

[13]  Michael Elad,et al.  Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit , 2008 .

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

[15]  Kjersti Engan,et al.  Family of iterative LS-based dictionary learning algorithms, ILS-DLA, for sparse signal representation , 2007, Digit. Signal Process..

[16]  Kjersti Engan,et al.  Method of optimal directions for frame design , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[17]  Michael Elad,et al.  Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation , 2010, IEEE Transactions on Signal Processing.

[18]  Sacha Krstulovic,et al.  Mptk: Matching Pursuit Made Tractable , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[19]  Michael Elad,et al.  Sparse and Redundant Modeling of Image Content Using an Image-Signature-Dictionary , 2008, SIAM J. Imaging Sci..

[20]  Mark D. Plumbley,et al.  Structure-aware dictionary learning with harmonic atoms , 2011, 2011 19th European Signal Processing Conference.

[21]  Martin Vetterli,et al.  Oversampled filter banks , 1998, IEEE Trans. Signal Process..

[22]  Pierre Vandergheynst,et al.  A low complexity Orthogonal Matching Pursuit for sparse signal approximation with shift-invariant dictionaries , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[23]  Pierre Vandergheynst,et al.  Shift-invariant dictionary learning for sparse representations: Extending K-SVD , 2008, 2008 16th European Signal Processing Conference.

[24]  Christoph Studer,et al.  Learning phase-invariant dictionaries , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.