Imposing shift-invariance using Flexible Structure Dictionary Learning (FSDL)

Sparse representation and Dictionary learning have attracted a lot of research attention in the last couple of decades and have provided state of the art results in many fields such as denoising, classification, inpainting and compression. However, applying general dictionary learning such as Method...

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Veröffentlicht in:Digital signal processing Jg. 69; S. 162 - 173
Hauptverfasser: Barzideh, Faraz, Skretting, Karl, Engan, Kjersti
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.10.2017
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ISSN:1051-2004, 1095-4333
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Abstract Sparse representation and Dictionary learning have attracted a lot of research attention in the last couple of decades and have provided state of the art results in many fields such as denoising, classification, inpainting and compression. However, applying general dictionary learning such as Method of Optimal Directions and Recursive Least Squares Dictionary Learning Algorithm can be computationally expensive, due to the large amount of free variables to be learned. Also sometimes the signal class has obvious repetitive structure which could benefit from a structured dictionary. One way to deal with these shortcomings is to impose a structure on the dictionary itself, for example the dictionary can be sparse or the atoms can be shift-invariant. In practice, imposing a structure means limiting the number of free variables. There are many examples of structured dictionaries such as double sparsity model or shift-invariant dictionaries. We have recently proposed a closed form solution to impose arbitrary structures onto a dictionary, called Flexible Structure Dictionary Learning. In this paper, we use this method to impose shift-invariant structure when training a dictionary. This structure allows us to not only simplify the original solution and make it computationally feasible to be used for large signals but also extend the concept of shift-invariance to include variable sized shifts in different atoms. The proposed dictionary update step finds all the free variables in all the atoms jointly, whereas some shift-invariant structured dictionaries in the recent literature, update one atom at a time. We have compared our proposed method with a general dictionary learning method and another shift-invariant method. Results show that signal approximation can be a promising application.
AbstractList Sparse representation and Dictionary learning have attracted a lot of research attention in the last couple of decades and have provided state of the art results in many fields such as denoising, classification, inpainting and compression. However, applying general dictionary learning such as Method of Optimal Directions and Recursive Least Squares Dictionary Learning Algorithm can be computationally expensive, due to the large amount of free variables to be learned. Also sometimes the signal class has obvious repetitive structure which could benefit from a structured dictionary. One way to deal with these shortcomings is to impose a structure on the dictionary itself, for example the dictionary can be sparse or the atoms can be shift-invariant. In practice, imposing a structure means limiting the number of free variables. There are many examples of structured dictionaries such as double sparsity model or shift-invariant dictionaries. We have recently proposed a closed form solution to impose arbitrary structures onto a dictionary, called Flexible Structure Dictionary Learning. In this paper, we use this method to impose shift-invariant structure when training a dictionary. This structure allows us to not only simplify the original solution and make it computationally feasible to be used for large signals but also extend the concept of shift-invariance to include variable sized shifts in different atoms. The proposed dictionary update step finds all the free variables in all the atoms jointly, whereas some shift-invariant structured dictionaries in the recent literature, update one atom at a time. We have compared our proposed method with a general dictionary learning method and another shift-invariant method. Results show that signal approximation can be a promising application.
Author Skretting, Karl
Barzideh, Faraz
Engan, Kjersti
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Cites_doi 10.1038/nature04485
10.1111/j.2517-6161.1996.tb02080.x
10.1109/TSP.2006.881199
10.1109/TBME.2011.2173935
10.1109/TSP.2010.2040671
10.1016/j.acha.2008.03.004
10.1109/83.841526
10.1109/TPAMI.2011.156
10.1161/01.CIR.101.23.e215
10.1109/TIP.2006.881969
10.1109/TSA.2005.860346
10.1016/S0377-0427(00)00393-9
10.1109/LSP.2013.2288788
10.1109/78.258082
10.1137/07070156X
10.1109/TIP.2007.911828
10.1109/TPAMI.2013.88
10.1109/TIP.2005.843753
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Keywords Sparse representation
Flexible Structure Dictionary learning
Dictionary learning
Shift-invariant dictionary
Language English
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References Mørup, Schmidt, Hansen (br0290) 2008
Zheng, Yang, Carbonell (br0320) 2016
Blumensath, Davies (br0280) 2006; 14
Mairal, Bach, Ponce (br0080) 2012; 34
Martin-del Campo, Sandin (br0130) 2015
Colomer, Naranjo, Engan, Skretting (br0100) 2015
Aharon, Elad (br0250) 2008; 1
Mallat (br0230) 2009; 26
Loan (br0330) 2000; 123
Jiang, Lin, Davis (br0060) 2013; 35
Skretting, Engan (br0200) 2010; 58
Mairal, Bach, Ponce, Sapiro (br0190) 2009
Rusu, Dumitrescu, Tsaftaris (br0240) 2014; 21
Mailhé, Lesage, Gribonval, Bimbot, Vandergheynst (br0310) 2008
Smith, Lewicki (br0260) 2006; 439
Barzideh, Skretting, Engan (br0270) 2015
Engan, Aase, Håkon Husøy (br0170) 1999
Blumensath, Davies (br0120) 2005
Tibshirani (br0160) 1996; 58
Thiagarajan, Ramamurthy, Spanias (br0300) 2008
Elad (br0140) 2010
Goldberger (br0340) June 13 2000; 101
Zhang, Li (br0090) 2010
Aharon, Elad, Bruckstein (br0180) 2006; 54
Pennec, Mallat (br0220) 2005; 14
Elad, Aharon (br0010) 2006; 15
Yang, Zhang, Feng, Zhang (br0070) 2011
Mallat, Zhang (br0150) 1993; 41
Mairal, Sapiro, Elad (br0020) 2007
Li, Fang, Yin (br0030) 2012; 59
Meyer, Averbuch, Stromberg (br0210) 2000; 9
Skretting, Engan (br0040) 2011
Grosse, Raina, Kwong, Ng (br0050) 2007
Mairal, Elad, Sapiro (br0110) 2008; 17
Elad (10.1016/j.dsp.2017.06.023_br0010) 2006; 15
Mairal (10.1016/j.dsp.2017.06.023_br0020) 2007
Li (10.1016/j.dsp.2017.06.023_br0030) 2012; 59
Smith (10.1016/j.dsp.2017.06.023_br0260) 2006; 439
Mairal (10.1016/j.dsp.2017.06.023_br0110) 2008; 17
Mallat (10.1016/j.dsp.2017.06.023_br0150) 1993; 41
Mairal (10.1016/j.dsp.2017.06.023_br0190) 2009
Zhang (10.1016/j.dsp.2017.06.023_br0090) 2010
Loan (10.1016/j.dsp.2017.06.023_br0330) 2000; 123
Blumensath (10.1016/j.dsp.2017.06.023_br0280) 2006; 14
Yang (10.1016/j.dsp.2017.06.023_br0070) 2011
Skretting (10.1016/j.dsp.2017.06.023_br0200) 2010; 58
Jiang (10.1016/j.dsp.2017.06.023_br0060) 2013; 35
Martin-del Campo (10.1016/j.dsp.2017.06.023_br0130) 2015
Mailhé (10.1016/j.dsp.2017.06.023_br0310) 2008
Goldberger (10.1016/j.dsp.2017.06.023_br0340) 2000; 101
Engan (10.1016/j.dsp.2017.06.023_br0170) 1999
Barzideh (10.1016/j.dsp.2017.06.023_br0270) 2015
Rusu (10.1016/j.dsp.2017.06.023_br0240) 2014; 21
Aharon (10.1016/j.dsp.2017.06.023_br0180) 2006; 54
Mairal (10.1016/j.dsp.2017.06.023_br0080) 2012; 34
Skretting (10.1016/j.dsp.2017.06.023_br0040) 2011
Thiagarajan (10.1016/j.dsp.2017.06.023_br0300) 2008
Blumensath (10.1016/j.dsp.2017.06.023_br0120) 2005
Grosse (10.1016/j.dsp.2017.06.023_br0050) 2007
Meyer (10.1016/j.dsp.2017.06.023_br0210) 2000; 9
Mallat (10.1016/j.dsp.2017.06.023_br0230) 2009; 26
Colomer (10.1016/j.dsp.2017.06.023_br0100) 2015
Zheng (10.1016/j.dsp.2017.06.023_br0320) 2016
Elad (10.1016/j.dsp.2017.06.023_br0140) 2010
Mørup (10.1016/j.dsp.2017.06.023_br0290) 2008
Pennec (10.1016/j.dsp.2017.06.023_br0220) 2005; 14
Aharon (10.1016/j.dsp.2017.06.023_br0250) 2008; 1
Tibshirani (10.1016/j.dsp.2017.06.023_br0160) 1996; 58
References_xml – start-page: 543
  year: 2011
  end-page: 550
  ident: br0070
  article-title: Fisher discrimination dictionary learning for sparse representation
  publication-title: 2011 International Conference on Computer Vision
– start-page: 2095
  year: 2016
  end-page: 2104
  ident: br0320
  article-title: Efficient shift-invariant dictionary learning
  publication-title: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
– start-page: 145
  year: 2008
  end-page: 150
  ident: br0300
  article-title: Shift-invariant sparse representation of images using learned dictionaries
  publication-title: 2008 IEEE Workshop on Machine Learning for Signal Processing
– volume: 439
  start-page: 978
  year: 2006
  end-page: 982
  ident: br0260
  article-title: Efficient auditory coding
  publication-title: Nature
– volume: 41
  start-page: 3397
  year: 1993
  end-page: 3415
  ident: br0150
  article-title: Matching pursuits with time-frequency dictionaries
  publication-title: IEEE Trans. Signal Process.
– start-page: 1
  year: 2008
  end-page: 5
  ident: br0310
  article-title: Shift-invariant dictionary learning for sparse representations: extending K-SVD
  publication-title: 2008 16th European Signal Processing Conference
– start-page: 429
  year: 2015
  end-page: 433
  ident: br0100
  article-title: Retinal vessel inpainting using recursive least square dictionary learning algorithm
  publication-title: 2015 International Conference on Image Processing Theory, Tools and Applications
– volume: 58
  start-page: 267
  year: 1996
  end-page: 288
  ident: br0160
  article-title: Regression shrinkage and selection via the lasso
  publication-title: J. R. Stat. Soc., Ser. B, Methodol.
– start-page: 2443
  year: 1999
  end-page: 2446
  ident: br0170
  article-title: Method of optimal directions for frame design
  publication-title: Proceedings 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5
– volume: 123
  start-page: 85
  year: 2000
  end-page: 100
  ident: br0330
  article-title: The ubiquitous Kronecker product
  publication-title: Numerical Analysis 2000, vol. III: Linear Algebra
– start-page: 1517
  year: 2011
  end-page: 1520
  ident: br0040
  article-title: Image compression using learned dictionaries by RLS-DLA and compared with K-SVD
  publication-title: IEEE International Conference on Acoustics, Speech and Signal Processing
– start-page: 75
  year: 2005
  end-page: 78
  ident: br0120
  article-title: Shift-invariant sparse coding for single channel blind source separation
  publication-title: Workshop on Signal Processing with Adaptive Sparse Structured Representations
– volume: 54
  start-page: 4311
  year: 2006
  end-page: 4322
  ident: br0180
  article-title: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation
  publication-title: IEEE Trans. Signal Process.
– volume: 59
  start-page: 417
  year: 2012
  end-page: 427
  ident: br0030
  article-title: An efficient dictionary learning algorithm and its application to 3-d medical image denoising
  publication-title: IEEE Trans. Biomed. Eng.
– year: 2007
  ident: br0020
  article-title: Multiscale sparse image representation with learned dictionaries
  publication-title: 2007 IEEE International Conference on Image Processing, vol. 3
– volume: 14
  start-page: 50
  year: 2006
  end-page: 57
  ident: br0280
  article-title: Sparse and shift-invariant representations of music
  publication-title: IEEE Trans. Audio Speech Lang. Process.
– volume: 58
  start-page: 2121
  year: 2010
  end-page: 2130
  ident: br0200
  article-title: Recursive least squares dictionary learning algorithm
  publication-title: IEEE Trans. Signal Process.
– volume: 101
  start-page: e215
  year: June 13 2000
  end-page: e220
  ident: br0340
  article-title: PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals
  publication-title: Circulation
– volume: 35
  start-page: 2651
  year: 2013
  end-page: 2664
  ident: br0060
  article-title: Label consistent K-SVD: learning a discriminative dictionary for recognition
  publication-title: IEEE Trans. Pattern Anal. Mach. Intell.
– start-page: 149
  year: 2007
  end-page: 158
  ident: br0050
  article-title: Shift-invariance sparse coding for audio classification
  publication-title: Proceedings of the Twenty-Third Conference Annual Conference on Uncertainty in Artificial Intelligence
– start-page: 1306
  year: 2015
  end-page: 1310
  ident: br0130
  article-title: Towards zero-configuration condition monitoring based on dictionary learning
  publication-title: 23rd European Signal Processing Conference
– start-page: 943
  year: 2015
  end-page: 947
  ident: br0270
  article-title: The flexible signature dictionary
  publication-title: 2015 23rd European Signal Processing Conference
– volume: 34
  start-page: 791
  year: 2012
  end-page: 804
  ident: br0080
  article-title: Task-driven dictionary learning
  publication-title: IEEE Trans. Pattern Anal. Mach. Intell.
– volume: 26
  start-page: 161
  year: 2009
  end-page: 180
  ident: br0230
  article-title: Geometrical grouplets
  publication-title: Appl. Comput. Harmon. Anal.
– volume: 17
  start-page: 53
  year: 2008
  end-page: 69
  ident: br0110
  article-title: Sparse representation for color image restoration
  publication-title: IEEE Trans. Image Process.
– start-page: 689
  year: 2009
  end-page: 696
  ident: br0190
  article-title: Online dictionary learning for sparse coding
  publication-title: Proceedings of the 26th Annual International Conference on Machine Learning
– volume: 1
  start-page: 228
  year: 2008
  end-page: 247
  ident: br0250
  article-title: Sparse and redundant modeling of image content using an image-signature-dictionary
  publication-title: SIAM J. Imaging Sci.
– volume: 21
  start-page: 6
  year: 2014
  end-page: 9
  ident: br0240
  article-title: Explicit shift-invariant dictionary learning
  publication-title: IEEE Signal Process. Lett.
– volume: 14
  start-page: 423
  year: 2005
  end-page: 438
  ident: br0220
  article-title: Sparse geometric image representations with bandelets
  publication-title: IEEE Trans. Image Process.
– year: 2010
  ident: br0140
  article-title: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
– start-page: 2691
  year: 2010
  end-page: 2698
  ident: br0090
  article-title: Discriminative K-SVD for dictionary learning in face recognition
  publication-title: 2010 IEEE Conference on Computer Vision and Pattern Recognition
– volume: 9
  start-page: 792
  year: 2000
  end-page: 800
  ident: br0210
  article-title: Fast adaptive wavelet packet image compression
  publication-title: IEEE Trans. Image Process.
– volume: 15
  start-page: 3736
  year: 2006
  end-page: 3745
  ident: br0010
  article-title: Image denoising via sparse and redundant representations over learned dictionaries
  publication-title: IEEE Trans. Image Process.
– year: 2008
  ident: br0290
  article-title: Shift Invariant Sparse Coding of Image And Music Data
– volume: 439
  start-page: 978
  year: 2006
  ident: 10.1016/j.dsp.2017.06.023_br0260
  article-title: Efficient auditory coding
  publication-title: Nature
  doi: 10.1038/nature04485
– start-page: 1306
  year: 2015
  ident: 10.1016/j.dsp.2017.06.023_br0130
  article-title: Towards zero-configuration condition monitoring based on dictionary learning
– volume: 58
  start-page: 267
  issue: 1
  year: 1996
  ident: 10.1016/j.dsp.2017.06.023_br0160
  article-title: Regression shrinkage and selection via the lasso
  publication-title: J. R. Stat. Soc., Ser. B, Methodol.
  doi: 10.1111/j.2517-6161.1996.tb02080.x
– start-page: 943
  year: 2015
  ident: 10.1016/j.dsp.2017.06.023_br0270
  article-title: The flexible signature dictionary
– start-page: 145
  year: 2008
  ident: 10.1016/j.dsp.2017.06.023_br0300
  article-title: Shift-invariant sparse representation of images using learned dictionaries
– start-page: 1517
  year: 2011
  ident: 10.1016/j.dsp.2017.06.023_br0040
  article-title: Image compression using learned dictionaries by RLS-DLA and compared with K-SVD
– start-page: 1
  year: 2008
  ident: 10.1016/j.dsp.2017.06.023_br0310
  article-title: Shift-invariant dictionary learning for sparse representations: extending K-SVD
– start-page: 2691
  year: 2010
  ident: 10.1016/j.dsp.2017.06.023_br0090
  article-title: Discriminative K-SVD for dictionary learning in face recognition
– year: 2010
  ident: 10.1016/j.dsp.2017.06.023_br0140
– volume: 54
  start-page: 4311
  issue: 11
  year: 2006
  ident: 10.1016/j.dsp.2017.06.023_br0180
  article-title: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2006.881199
– volume: 59
  start-page: 417
  issue: 2
  year: 2012
  ident: 10.1016/j.dsp.2017.06.023_br0030
  article-title: An efficient dictionary learning algorithm and its application to 3-d medical image denoising
  publication-title: IEEE Trans. Biomed. Eng.
  doi: 10.1109/TBME.2011.2173935
– volume: 58
  start-page: 2121
  issue: 4
  year: 2010
  ident: 10.1016/j.dsp.2017.06.023_br0200
  article-title: Recursive least squares dictionary learning algorithm
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/TSP.2010.2040671
– volume: 26
  start-page: 161
  issue: 2
  year: 2009
  ident: 10.1016/j.dsp.2017.06.023_br0230
  article-title: Geometrical grouplets
  publication-title: Appl. Comput. Harmon. Anal.
  doi: 10.1016/j.acha.2008.03.004
– volume: 9
  start-page: 792
  issue: 5
  year: 2000
  ident: 10.1016/j.dsp.2017.06.023_br0210
  article-title: Fast adaptive wavelet packet image compression
  publication-title: IEEE Trans. Image Process.
  doi: 10.1109/83.841526
– volume: 34
  start-page: 791
  issue: 4
  year: 2012
  ident: 10.1016/j.dsp.2017.06.023_br0080
  article-title: Task-driven dictionary learning
  publication-title: IEEE Trans. Pattern Anal. Mach. Intell.
  doi: 10.1109/TPAMI.2011.156
– volume: 101
  start-page: e215
  issue: 23
  year: 2000
  ident: 10.1016/j.dsp.2017.06.023_br0340
  article-title: PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals
  publication-title: Circulation
  doi: 10.1161/01.CIR.101.23.e215
– volume: 15
  start-page: 3736
  issue: 12
  year: 2006
  ident: 10.1016/j.dsp.2017.06.023_br0010
  article-title: Image denoising via sparse and redundant representations over learned dictionaries
  publication-title: IEEE Trans. Image Process.
  doi: 10.1109/TIP.2006.881969
– volume: 14
  start-page: 50
  issue: 1
  year: 2006
  ident: 10.1016/j.dsp.2017.06.023_br0280
  article-title: Sparse and shift-invariant representations of music
  publication-title: IEEE Trans. Audio Speech Lang. Process.
  doi: 10.1109/TSA.2005.860346
– start-page: 2095
  year: 2016
  ident: 10.1016/j.dsp.2017.06.023_br0320
  article-title: Efficient shift-invariant dictionary learning
– volume: 123
  start-page: 85
  issue: 1–2
  year: 2000
  ident: 10.1016/j.dsp.2017.06.023_br0330
  article-title: The ubiquitous Kronecker product
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/S0377-0427(00)00393-9
– volume: 21
  start-page: 6
  issue: 1
  year: 2014
  ident: 10.1016/j.dsp.2017.06.023_br0240
  article-title: Explicit shift-invariant dictionary learning
  publication-title: IEEE Signal Process. Lett.
  doi: 10.1109/LSP.2013.2288788
– year: 2008
  ident: 10.1016/j.dsp.2017.06.023_br0290
– start-page: 543
  year: 2011
  ident: 10.1016/j.dsp.2017.06.023_br0070
  article-title: Fisher discrimination dictionary learning for sparse representation
– start-page: 689
  year: 2009
  ident: 10.1016/j.dsp.2017.06.023_br0190
  article-title: Online dictionary learning for sparse coding
– start-page: 149
  year: 2007
  ident: 10.1016/j.dsp.2017.06.023_br0050
  article-title: Shift-invariance sparse coding for audio classification
– volume: 41
  start-page: 3397
  issue: 12
  year: 1993
  ident: 10.1016/j.dsp.2017.06.023_br0150
  article-title: Matching pursuits with time-frequency dictionaries
  publication-title: IEEE Trans. Signal Process.
  doi: 10.1109/78.258082
– start-page: 2443
  year: 1999
  ident: 10.1016/j.dsp.2017.06.023_br0170
  article-title: Method of optimal directions for frame design
– volume: 1
  start-page: 228
  issue: 3
  year: 2008
  ident: 10.1016/j.dsp.2017.06.023_br0250
  article-title: Sparse and redundant modeling of image content using an image-signature-dictionary
  publication-title: SIAM J. Imaging Sci.
  doi: 10.1137/07070156X
– year: 2007
  ident: 10.1016/j.dsp.2017.06.023_br0020
  article-title: Multiscale sparse image representation with learned dictionaries
– start-page: 429
  year: 2015
  ident: 10.1016/j.dsp.2017.06.023_br0100
  article-title: Retinal vessel inpainting using recursive least square dictionary learning algorithm
– volume: 17
  start-page: 53
  issue: 1
  year: 2008
  ident: 10.1016/j.dsp.2017.06.023_br0110
  article-title: Sparse representation for color image restoration
  publication-title: IEEE Trans. Image Process.
  doi: 10.1109/TIP.2007.911828
– volume: 35
  start-page: 2651
  issue: 11
  year: 2013
  ident: 10.1016/j.dsp.2017.06.023_br0060
  article-title: Label consistent K-SVD: learning a discriminative dictionary for recognition
  publication-title: IEEE Trans. Pattern Anal. Mach. Intell.
  doi: 10.1109/TPAMI.2013.88
– volume: 14
  start-page: 423
  issue: 4
  year: 2005
  ident: 10.1016/j.dsp.2017.06.023_br0220
  article-title: Sparse geometric image representations with bandelets
  publication-title: IEEE Trans. Image Process.
  doi: 10.1109/TIP.2005.843753
– start-page: 75
  year: 2005
  ident: 10.1016/j.dsp.2017.06.023_br0120
  article-title: Shift-invariant sparse coding for single channel blind source separation
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Snippet Sparse representation and Dictionary learning have attracted a lot of research attention in the last couple of decades and have provided state of the art...
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SubjectTerms Dictionary learning
Flexible Structure Dictionary learning
Shift-invariant dictionary
Sparse representation
Title Imposing shift-invariance using Flexible Structure Dictionary Learning (FSDL)
URI https://dx.doi.org/10.1016/j.dsp.2017.06.023
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