Sparse Representations, Compressive Sensing and dictionaries for pattern recognition

In recent years, the theories of Compressive Sensing (CS), Sparse Representation (SR) and Dictionary Learning (DL) have emerged as powerful tools for efficiently processing data in non-traditional ways. An area of promise for these theories is object recognition. In this paper, we review the role of SR, CS and DL for object recognition. Algorithms to perform object recognition using these theories are reviewed. An important aspect in object recognition is feature extraction. Recent works in SR and CS have shown that if sparsity in the recognition problem is properly harnessed then the choice of features is less critical. What becomes critical, however, is the number of features and the sparsity of representation. This issue is discussed in detail.

[1]  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).

[2]  David J. Kriegman,et al.  From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Guillermo Sapiro,et al.  Sparse representations for image classification: learning discriminative and reconstructive non-parametric dictionaries , 2008 .

[4]  Rama Chellappa,et al.  Appearance Characterization of Linear Lambertian Objects, Generalized Photometric Stereo, and Illumination-Invariant Face Recognition , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Guillermo Sapiro,et al.  Supervised Dictionary Learning , 2008, NIPS.

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

[7]  Rama Chellappa,et al.  Robust Estimation of Albedo for Illumination-invariant Matching and Shape Recovery , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[8]  Michael Elad,et al.  Dictionaries for Sparse Representation Modeling , 2010, Proceedings of the IEEE.

[9]  Xiaofei He,et al.  Locality Preserving Projections , 2003, NIPS.

[10]  Ke Huang,et al.  Sparse Representation for Signal Classification , 2006, NIPS.

[11]  Rama Chellappa,et al.  Sparse dictionary-based representation and recognition of action attributes , 2011, 2011 International Conference on Computer Vision.

[12]  R. DeVore,et al.  A Simple Proof of the Restricted Isometry Property for Random Matrices , 2008 .

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

[14]  Rama Chellappa,et al.  Separability-based multiscale basis selection and feature extraction for signal and image classification , 1998, IEEE Trans. Image Process..

[15]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[16]  Rama Chellappa,et al.  Secure and Robust Iris Recognition Using Random Projections and Sparse Representations , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[18]  Terence Sim,et al.  The CMU Pose, Illumination, and Expression Database , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Guillermo Sapiro,et al.  Sparse Representation for Computer Vision and Pattern Recognition , 2010, Proceedings of the IEEE.

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

[21]  Pascal Frossard,et al.  Semantic Coding by Supervised Dimensionality Reduction , 2008, IEEE Transactions on Multimedia.

[22]  Dimitris Achlioptas,et al.  Database-friendly random projections , 2001, PODS.

[23]  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.

[24]  Guillermo Sapiro,et al.  Discriminative learned dictionaries for local image analysis , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[25]  Marc'Aurelio Ranzato,et al.  Efficient Learning of Sparse Representations with an Energy-Based Model , 2006, NIPS.

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

[27]  Martial Hebert,et al.  Discriminative Sparse Image Models for Class-Specific Edge Detection and Image Interpretation , 2008, ECCV.

[28]  Marc'Aurelio Ranzato,et al.  Unsupervised Learning of Invariant Feature Hierarchies with Applications to Object Recognition , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[29]  Rama Chellappa,et al.  Illumination robust dictionary-based face recognition , 2011, 2011 18th IEEE International Conference on Image Processing.

[30]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[31]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[33]  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.

[34]  Michael Elad,et al.  On the Role of Sparse and Redundant Representations in Image Processing , 2010, Proceedings of the IEEE.

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

[36]  Larry S. Davis,et al.  Learning a discriminative dictionary for sparse coding via label consistent K-SVD , 2011, CVPR 2011.

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