References

1

Michal Šorel and Filip Šroubek. Fast convolutional sparse coding using matrix inversion lemma. Digital Signal Processing, 55:44–51, 2016. doi:10.1016/j.dsp.2016.04.012.

2

Manya V. Afonso, José M. Bioucas-Dias, and Mário A. T. Figueiredo. An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Transactions on Image Processing, 20(3):681–695, March 2011. doi:10.1109/tip.2010.2076294.

3

Stefano Alliney. Digital filters as absolute norm regularizers. IEEE Transactions on Signal Processing, 40(6):1548–1562, June 1992. doi:10.1109/78.139258.

4

Jonathan Barzilai and Jonathan M. Borwein. Two-point step size gradient methods. IMA Journal of Numerical Analysis, 8:141–148, 1988.

5

Amir Beck. First-Order Methods in Optimization. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2017. doi:10.1137/1.9781611974997.

6

Amir Beck and Marc Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183–202, 2009. doi:10.1137/080716542.

7

Amir Beck and Marc Teboulle. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Transactions on Image Processing, 18(11):2419–2434, 2009.

8

Peter Blomgren and Tony F. Chan. Color TV: total variation methods for restoration of vector-valued images. IEEE Transactions on Image Processing, 7(3):304–309, March 1998. doi:10.1109/83.661180.

9

Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1):1–122, 2010. doi:10.1561/2200000016.

10

Gregery T. Buzzard, Stanley H. Chan, Suhas Sreehari, and Charles A. Bouman. Plug-and-play unplugged: optimization-free reconstruction using consensus equilibrium. SIAM Journal on Imaging Sciences, 11(3):2001–2020, 2018. doi:10.1137/17M1122451.

11

Jian-Feng Cai, Emmanuel J. Candès, and Zuowei Shen. A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 20(4):1956–1982, 2010. doi:10.1137/080738970.

12

Emmanuel J. Candès, Xiaodong Li, Yi Ma, and John Wright. Robust principal component analysis? Journal of the ACM, 58:11:1–11:37, June 2011. doi:10.1145/1970392.1970395.

13

Rakesh Chalasani, Jose C. Principe, and Naveen Ramakrishnan. A fast proximal method for convolutional sparse coding. In Proceedings of the International Joint Conference on Neural Networks (IJCNN). August 2013. doi:10.1109/IJCNN.2013.6706854.

14

Antonin Chambolle and Charles Dossal. On the convergence of the iterates of "Fast Iterative Shrinkage/Thresholding Algorithm". Journal of Optimization Theory and Applications, 166:968–982, 2015. doi:10.1007/s10957-015-0746-4.

15

Rick Chartrand and Brendt Wohlberg. A nonconvex ADMM algorithm for group sparsity with sparse groups. In Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 6009–6013. May 2013. doi:10.1109/ICASSP.2013.6638818.

16

Scott Shaobing Chen, David L. Donoho, and Michael A. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1):33–61, 1998. doi:10.1137/S1064827596304010.

17

Andrea Cogliati, Zhiyao Duan, and Brendt Wohlberg. Piano transcription with convolutional sparse lateral inhibition. IEEE Signal Processing Letters, 24(4):392–396, April 2017. doi:10.1109/LSP.2017.2666183.

18

Kostadin Dabov, Alessandro Foi, Vladimir Katkovnik, and Karen Egiazarian. Image restoration by sparse 3D transform-domain collaborative filtering. In Jaakko T. Astola, Karen O. Egiazarian, and Edward R. Dougherty, editors, Image Processing: Algorithms and Systems VI, volume 6812, 62–73. International Society for Optics and Photonics, SPIE, 2008. doi:10.1117/12.766355.

19

John Duchi, Shai Shalev-Shwartz, Yoram Singer, and Tushar Chandra. Efficient projections onto the $\ell _1$-ball for learning in high dimensions. In Proceedings of the 25th International Conference on Machine Learning (ICML), 272–279. 2008. doi:10.1145/1390156.1390191.

20

Kjersti Engan, Sven Ole Aase, and John Håkon Husøy. Method of optimal directions for frame design. In Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), volume 5, 2443–2446. 1999. doi:10.1109/icassp.1999.760624.

21

Ernie Esser. Primal Dual Algorithms for Convex Models and Applications to Image Restoration, Registration and Nonlocal Inpainting. PhD thesis, University of California Los Angeles, 2010.

22

Mihai I. Florea and Sergiy A. Vorobyov. A robust FISTA-like algorithm. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 4521–4525. 2017. doi:10.1109/ICASSP.2017.7953012.

23

Damien Garcia. Robust smoothing of gridded data in one and higher dimensions with missing values. Computational Statistics & Data Analysis, 54(4):1167–1178, 2010. doi:10.1016/j.csda.2009.09.020.

24

Cristina Garcia-Cardona and Brendt Wohlberg. Subproblem coupling in convolutional dictionary learning. In Proceedings of IEEE International Conference on Image Processing (ICIP), 1697–1701. Beijing, China, September 2017. doi:10.1109/ICIP.2017.8296571.

25

Cristina Garcia-Cardona and Brendt Wohlberg. Convolutional dictionary learning for multi-channel signals. In Proceedings of the 2018 Asilomar Conference on Signals, Systems, and Computers, 335–342. Pacific Grove, CA, USA, October 2018. doi:10.1109/ACSSC.2018.8645108.

26

Cristina Garcia-Cardona and Brendt Wohlberg. Convolutional dictionary learning: a comparative review and new algorithms. IEEE Transactions on Computational Imaging, 4(3):366–381, September 2018. arXiv:1709.02893, doi:10.1109/TCI.2018.2840334.

27

Tom Goldstein and Stanley Osher. The split Bregman method for l1-regularized problems. SIAM Journal on Imaging Sciences, 2(2):323–343, 2009. doi:10.1137/080725891.

28

Felix Heide, Wolfgang Heidrich, and Gordon Wetzstein. Fast and flexible convolutional sparse coding. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 5135–5143. 2015. doi:10.1109/CVPR.2015.7299149.

29

Kevin Jarrett, Koray Kavukcuoglu, Marc'Aurelio Ranzato, and Yann LeCun. What is the best multi-stage architecture for object recognition? In IEEE International Conference on Computer Vision (ICCV), 2146–2153. September 2009. doi:10.1109/ICCV.2009.5459469.

30

Ulugbek Kamilov, Hassan Mansour, and Brendt Wohlberg. A plug-and-play priors approach for solving nonlinear imaging inverse problems. IEEE Signal Processing Letters, 24(12):1872–1876, December 2017. doi:10.1109/LSP.2017.2763583.

31

Matthieu Kowalski. Sparse regression using mixed norms. Applied and Computational Harmonic Analysis, 27(3):303–324, 2009. doi:10.1016/j.acha.2009.05.006.

32

Matthieu Kowalski. Thresholding rules and iterative shrinkage/thresholding algorithm: a convergence study. In IEEE International Conference on Image Processing (ICIP), 4151–4155. October 2014. doi:10.1109/ICIP.2014.7025843.

33

Jialin Liu, Cristina Garcia-Cardona, Brendt Wohlberg, and Wotao Yin. First and second order methods for online convolutional dictionary learning. SIAM Journal on Imaging Sciences, 11(2):1589–1628, 2018. arXiv:1709.00106, doi:10.1137/17M1145689.

34

Yifei Lou and Ming Yan. Fast L1-L2 minimization via a proximal operator. Journal of Scientific Computing, 74(2):767–785, 2018. doi:10.1007/s10915-017-0463-2.

35

Ymir Mäkinen, Lucio Azzari, and Alessandro Foi. Exact transform-domain noise variance for collaborative filtering of stationary correlated noise. In IEEE International Conference on Image Processing (ICIP), 185–189. September 2019. doi:10.1109/ICIP.2019.8802964.

36

Julien Mairal, Francis Bach, and Jean Ponce. Sparse modeling for image and vision processing. Foundations and Trends in Computer Graphics and Vision, 8(2-3):85–283, 2014. doi:10.1561/0600000058.

37

Daniele Menon, Stefano Andriani, and Giancarlo Calvagno. Demosaicing with directional filtering and a posteriori decision. IEEE Transactions on Image Processing, 16(1):132–141, January 2007. doi:10.1109/tip.2006.884928.

38

Ryosuke Okuta, Yuya Unno, Daisuke Nishino, Shohei Hido, and Crissman Loomis. CuPy: a NumPy-compatible library for NVIDIA GPU calculations. In Proceedings of Workshop on Machine Learning Systems (LearningSys) in The Thirty-first Annual Conference on Neural Information Processing Systems (NIPS). 2017. URL: http://learningsys.org/nips17/assets/papers/paper_16.pdf.

39

Neal Parikh and Stephen Boyd. Proximal algorithms. Foundations and Trends in Optimization, 1(3):127–239, 2014. doi:10.1561/2400000003.

40

Paul Rodriguez. Improving FISTA's speed of convergence via a novel inertial sequence. In Proceedings of 27th European Signal Processing Conference (EUSIPCO). 2019.

41

Leonid I. Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 60(1–4):259–268, 1992. doi:10.1016/0167-2789(92)90242-F.

42

Erik Skau and Brendt Wohlberg. A fast parallel algorithm for convolutional sparse coding. In Proceedings of the IEEE Image, Video, and Multidimensional Signal Processing Workshop (IVMSP). June 2018. doi:10.1109/IVMSPW.2018.8448536.

43

Suvrit Sra. Fast Projections onto $\ell _1,q$-Norm Balls for Grouped Feature Selection, pages 305–317. Springer, 2011. doi:10.1007/978-3-642-23808-6_20.

44

Suhas Sreehari, Singanallur V. Venkatakrishnan, Brendt Wohlberg, Gregery T. Buzzard, Lawrence F. Drummy, Jeffrey P. Simmons, and Charles A. Bouman. Plug-and-play priors for bright field electron tomography and sparse interpolation. IEEE Transactions on Computational Imaging, 2(4):408–423, December 2016. doi:10.1109/TCI.2016.2599778.

45

Mariano Tepper and Guillermo Sapiro. Fast l1 smoothing splines with an application to kinect depth data. In Proceedings of IEEE International Conference on Image Processing (ICIP), 504–508. September 2013. doi:10.1109/ICIP.2013.6738104.

46

Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1):267–288, 1996. URL: http://www.jstor.org/stable/2346178.

47

Charles F. Van Loan. The ubiquitous Kronecker product. Journal of Computational and Applied Mathematics, 123(1–2):85–100, November 2000. doi:10.1016/S0377-0427(00)00393-9.

48

Singanallur V. Venkatakrishnan, Charles A. Bouman, and Brendt Wohlberg. Plug-and-play priors for model based reconstruction. In Proceedings of IEEE Global Conference on Signal and Information Processing (GlobalSIP), 945–948. Austin, TX, USA, December 2013. doi:10.1109/GlobalSIP.2013.6737048.

49

Brendt Wohlberg. Efficient convolutional sparse coding. In Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 7173–7177. May 2014. doi:10.1109/ICASSP.2014.6854992.

50

Brendt Wohlberg. Boundary handling for convolutional sparse representations. In Proceedings of IEEE International Conference on Image Processing (ICIP), 1833–1837. September 2016. doi:10.1109/ICIP.2016.7532675.

51

Brendt Wohlberg. Convolutional sparse representation of color images. In Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI), 57–60. March 2016. doi:10.1109/SSIAI.2016.7459174.

52

Brendt Wohlberg. Convolutional sparse representations as an image model for impulse noise restoration. In Proceedings of the IEEE Image, Video, and Multidimensional Signal Processing Workshop (IVMSP). July 2016. doi:10.1109/IVMSPW.2016.7528229.

53

Brendt Wohlberg. Efficient algorithms for convolutional sparse representations. IEEE Transactions on Image Processing, 25(1):301–315, January 2016. doi:10.1109/TIP.2015.2495260.

54

Brendt Wohlberg. SParse Optimization Research COde (SPORCO). Software library available from http://purl.org/brendt/software/sporco, 2016.

55

Brendt Wohlberg. Convolutional sparse coding with overlapping group norms. August 2017. arXiv:1708.09038.

56

Brendt Wohlberg. ADMM penalty parameter selection by residual balancing. April 2017. arXiv:1704.06209.

57

Brendt Wohlberg. SPORCO: A Python package for standard and convolutional sparse representations. In Proceedings of the 15th Python in Science Conference, 1–8. Austin, TX, USA, July 2017. doi:10.25080/shinma-7f4c6e7-001.

58

Brendt Wohlberg. Convolutional sparse representations with gradient penalties. In Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 6528–6532. Calgary, Alberta, Canada, 2018. arXiv:1705.04407, doi:10.1109/ICASSP.2018.8462151.

59

Brendt Wohlberg, Rick Chartrand, and James Theiler. Local principal component pursuit for nonlinear datasets. In Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 3925–3928. Kyoto, Japan, March 2012. doi:10.1109/ICASSP.2012.6288776.

60

Brendt Wohlberg and Paul Rodríguez. Convolutional sparse coding: boundary handling revisited. July 2017. arXiv:1707.06718.

61

Wufeng Xue, Xuanqin Mou, Lei Zhang, and Xiangchu Feng. Perceptual fidelity aware mean squared error. In IEEE International Conference on Computer Vision, 705–712. December 2013. doi:10.1109/ICCV.2013.93.

62

Wufeng Xue, Lei Zhang, Xuanqin Mou, and Alan C. Bovik. Gradient magnitude similarity deviation: a highly efficient perceptual image quality index. IEEE Transactions on Image Processing, 23(2):684–695, February 2014. doi:10.1109/TIP.2013.2293423.

63

Ya-xiang Yuan. Step-sizes for the gradient method. In AMS/IP Studies in Advanced Mathematics, volume 42, 785–796. 2008.

64

Hui Zou and Trevor Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2):301–320, 2005. doi:10.1111/j.1467-9868.2005.00503.x.