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 |
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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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Faraz surname: Barzideh fullname: Barzideh, Faraz email: faraz.barzideh@gmail.com, faraz.barzideh@uis.no – sequence: 2 givenname: Karl surname: Skretting fullname: Skretting, Karl email: karl.skretting@uis.no – sequence: 3 givenname: Kjersti orcidid: 0000-0002-8970-0067 surname: Engan fullname: Engan, Kjersti email: kjersti.engan@uis.no |
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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 |
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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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| SubjectTerms | Dictionary learning Flexible Structure Dictionary learning Shift-invariant dictionary Sparse representation |
| Title | Imposing shift-invariance using Flexible Structure Dictionary Learning (FSDL) |
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