Abstract
Purpose
Image models are central to all image processing tasks. The great advancements in digital image processing would not have been made possible without powerful models which, themselves, have evolved over time. In the past decade, “patch-based” models have emerged as one of the most effective models for natural images. Patch-based methods have outperformed other competing methods in many image processing tasks. These developments have come at a time when greater availability of powerful computational resources and growing concerns over the health risks of the ionizing radiation encourage research on image processing algorithms for computed tomography (CT). The goal of this paper is to explain the principles of patch-based methods and to review some of their recent applications in CT.
Methods
We first review the central concepts in patch-based image processing and explain some of the state-of-the-art algorithms, with a focus on aspects that are more relevant to CT. Then, we review some of the recent application of patch-based methods in CT.
Results
Patch-based methods have already transformed the field of image processing, leading to state-of-the-art results in many applications. More recently, several studies have proposed patch-based algorithms for various image processing tasks in CT, from denoising and restoration to iterative reconstruction. Although these studies have reported good results, the true potential of patch-based methods for CT has not been yet appreciated.
Conclusions
Patch-based methods can play a central role in image reconstruction and processing for CT. They have the potential to lead to substantial improvements in the current state of the art.
Similar content being viewed by others
References
Aharon M, Elad M (2008) Sparse and redundant modeling of image content using an image-signature-dictionary. SIAM J Imaging Sci 1(3):228–247
Aharon M, Elad M, Bruckstein A (2006) K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54(11):4311–4322
AlAfeef A, Cockshott P, MacLaren I, McVitie S (2014) Compressed sensing electron tomography using adaptive dictionaries: a simulation study. J Phys: Conf Ser 522(1):012021
Bach F, Jenatton R, Mairal J, Obozinski G (2012) Optimization with sparsity-inducing penalties. Found Trends Mach Learn 4(1):1–106
Barnes C, Shechtman E, Goldman D, Finkelstein A (2010) The generalized patchmatch correspondence algorithm. In: Daniilidis K, Maragos P, Paragios N (eds) Computer vision ECCV 2010, vol 6313, lecture notes in computer ScienceSpringer, Berlin, pp 29–43
Borsdorf A, Köstler H, Rubinstein R, Bartuschat D, Strmer M (2009) A parallel K-SVD implementation for CT image denoising. Technical Report CS 10, University of Erlangen-Nurnberg
Bian Z, Ma J, Huang J, Zhang H, Niu S, Feng Q, Liang Z, Chen W (2013) Sr-nlm: a sinogram restoration induced non-local means image filtering for low-dose computed tomography. Comput Med Imaging Graph 37(4):293–303
Buades A, Coll B, Morel J-M (2005) A review of image denoising algorithms, with a new one. Multiscale Model Simul 4(2):490–530
Buades A, Coll B, Morel J-M (2006) Image enhancement by non-local reverse heat equation. Preprint CMLA 22:2006
Chainais P (Sept 2012) Towards dictionary learning from images with non gaussian noise. In: 2012 IEEE international workshop on machine learning for signal processing (MLSP), pp 1–6
Chatterjee P, Milanfar P (2010) Is denoising dead? IEEE Trans Image Process 19(4):895–911
Chatterjee P, Milanfar P (2012) Patch-based near-optimal image denoising. IEEE Trans Image Process 21(4):1635–1649
Chen Y, Chen W, Yin X, Ye X, Bao X, Luo L, Feng Q, li Y, Yu X (2011) Improving low-dose abdominal CT images by weighted intensity averaging over large-scale neighborhoods. Eur J Radiol 80(2):e42–e49
Chen Y, Gao D, Nie C, Luo L, Chen W, Yin X, Lin Y (2009) Bayesian statistical reconstruction for low-dose X-ray computed tomography using an adaptive-weighting nonlocal prior. Comput Med Imaging Graph 33(7):495–500
Chen Y, Shi L, Feng Q, Yang J, Shu H, Luo L, Coatrieux J-L, Chen W (2014) Artifact suppressed dictionary learning for low-dose CT image processing. IEEE Trans Med Imaging 33(12):2271–2292
Chen Y, Shi L, Yang J, Hu Y, Luo L, Yin X, Coatrieux J-L (2014) Radiation dose reduction with dictionary learning based processing for head CT. Australas Phys Eng Sci Med 37(3):483–493
Chen Y, Yang Z, Hu Y, Yang G, Zhu Y, Li Y, luo L, Chen W, Toumoulin C (2012) Thoracic low-dose CT image processing using an artifact suppressed large-scale nonlocal means. Phys Med Biol 57(9):2667
Chen Y, Yin X, Shi L, Shu H, Luo L, Coatrieux J-L, Toumoulin C (2013) Improving abdomen tumor low-dose CT images using a fast dictionary learning based processing. Phys Med Biol 58(16):5803
Couzinie-Devy F, Mairal J, Bach F, Ponce J (2011) Dictionary learning for deblurring and digital zoom. Preprint. arXiv:1110.0957
Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–2095
Darbon J, Cunha A, Chan T, Osher S, Jensen G (2008) Fast nonlocal filtering applied to electron cryomicroscopy. In: 5th IEEE international symposium on biomedical imaging: from Nano to Macro, 2008. ISBI 2008, pp 1331–1334, May
Deledalle C-A, Denis L, Tupin F (2012) How to compare noisy patches? patch similarity beyond gaussian noise. Int J Comput Vis 99(1):86–102
Deledalle C-A, Duval V, Salmon J (2012) Non-local methods with shape-adaptive patches (NLM-SAP). J Math Imaging Vis 43(2):103–120
Deledalle C-A, Salmon J, Dalalyan A (2011) Image denoising with patch based PCA: local versus global. BMVC 81:425–455
Deledalle C-A, Tupin F, Denis L (Sept 2010) Poisson NL means: unsupervised non local means for poisson noise. In: 17th IEEE international conference on image processing (ICIP), 2010, pp 801–804
Deledalle C-A, Tupin F, Denis L (Sept 2011) Patch similarity under non Gaussian noise. In: International conference on image processing. Brussels, pp 1845–1848
Dong W, Zhang D, Shi G, Wu X (2011) Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans Image Process 20(7):1838–1857
Dore V, Cheriet M (2009) Robust NL-means filter with optimal pixel-wise smoothing parameter for statistical image denoising. IEEE Trans Signal Process 57(5):1703–1716
Dupe F-X, Anthoine S (Sept 2013) A greedy approach to sparse poisson denoising. In: 2013 IEEE international workshop on machine learning for signal processing (MLSP), pp 1–6
Elad M (2010) Sparse and redundant representations: from theory to applications in signal and image processing. Springer, Berlin
Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736–3745
Engan K, Aase S, Hakon Husoy J (1999) Method of optimal directions for frame design. In 1999. Proceedings, 1999 IEEE international conference on acoustics, speech, and signal processing, vol 5, pp 2443–2446
Etter V, Jovanovic I, Vetterli M (2011) Use of learned dictionaries in tomographic reconstruction. In: SPIE optical engineering+ applications, International Society for Optics and Photonics, pp 81381C–81381C-11
Giryes R, Elad M (2013) Sparsity based poisson denoising with dictionary learning. Preprint. arXiv:1309.4306
Gregor K, Lecun Y (2010) Learning fast approximations of sparse coding. In: 2010 international conference on machine learning (ICML), Omnipress, pp 1–8
Hawe S, Seibert M, Kleinsteuber M (2013) Separable dictionary learning. In: 2013 IEEE conference on computer vision and pattern recognition (CVPR), IEEE, pp 438–445
Huang D-A, Wang Y-CF (2013) Coupled dictionary and feature space learning with applications to cross-domain image synthesis and recognition. In: 2013 IEEE international conference on computer vision (ICCV), IEEE, pp 2496–2503
Huang J, Ma J, Liu N, Zhang H, Bian Z, Feng Y, Feng Q, Chen W (2011) Sparse angular CT reconstruction using non-local means based iterative-correction POCS. Comput Biol Med 41(4):195–205
Jenatton R, Mairal J, Bach FR, Obozinski GR (2010) Proximal methods for sparse hierarchical dictionary learning. In: Proceedings of the 27th international conference on machine learning (ICML-10), pp 487–494
Jia X, Tian Z, Lou Y, Sonke J-J, Jiang SB (2012) Four-dimensional cone beam CT reconstruction and enhancement using a temporal nonlocal means method. Med Phys 39(9):5592–5602
Kang L-W, Lin C-W, Fu Y-H (2012) Automatic single-image-based rain streaks removal via image decomposition. IEEE Trans Image Process 21(4):1742–1755
Karimi D, Ward RK (2016) A novel structured dictionary for fast processing of 3D medical images, with application to computed tomography restoration and denoising. In: SPIE medical imaging, International Society for Optics and Photonics, pp 97840N–97840N-7
Karimi D, Ward R (2016) Reducing streak artifacts in computed tomography via sparse representation in coupled dictionaries. Med Phys 43(3):1473–1486
Karimi D, Ward R, Ford N (Sept 2015) Angular upsampling of projection measurements in 3D computed tomography using a sparsity prior. In: 2015 IEEE international conference on image processing (ICIP), pp 3363–3367
Karimi D, Ward RK (2016) Sinogram denoising via simultaneous sparse representation in learned dictionaries. Phys Med Biol 61(9):3536–3553
Kavukcuoglu K, Ranzato M, Fergus R, Le-Cun Y (June 2009) Learning invariant features through topographic filter maps. In: IEEE conference on computer vision and pattern recognition, 2009. CVPR 2009, pp 1605–1612
Kazantsev D, Thompson WM, Van Eyndhoven G, Dobson K, Kaestner AP, Lionheart W, Withers PJ, Lee PD (2015) 4D-CT reconstruction with unified spatial-temporal patch-based regularization. Inverse Probl. Imaging 9:447–467
Kazantsev D, Van Eyndhoven G, Lionheart W, Withers P, Dobson K, McDonald S, Atwood R, Lee P (2015) Employing temporal self-similarity across the entire time domain in computed tomography reconstruction. Philos Trans R Soc Lond A 373(2043):20140389
Kelm Z, Blezek D, Bartholmai B, Erickson B (June 2009) Optimizing non-local means for denoising low dose CT. In: IEEE international symposium on biomedical imaging: from Nano to Macro, 2009. ISBI ’09, pp 662–665
Kindermann S, Osher S, Jones PW (2005) Deblurring and denoising of images by nonlocal functionals. Multiscale Model Simul 4(4):1091–1115
Kumar N, Zhang L, Nayar SK (Oct 2008) What is a good nearest neighbors algorithm for finding similar patches in images? In: European conference on computer vision (ECCV), pp 364–378
Lebrun M, Buades A, Morel JM (2013) A nonlocal Bayesian image denoising algorithm. SIAM J Imaging Sci 6(3):1665–1688
Lee H, Battle A, Raina R, Ng AY (2006) Efficient sparse coding algorithms. In: Advances in neural information processing systems, pp 801–808
Lewicki MS, Olshausen BA (1999) Probabilistic framework for the adaptation and comparison of image codes. JOSA A 16(7):1587–1601
Li S, Cao Q, Chen Y, Hu Y, Luo L, Toumoulin C (2014) Dictionary learning based sinogram inpainting for CT sparse reconstruction. Optik Int J Light Electron Optics 125(12):2862–2867
Li S, Fang L, Yin H (2012) An efficient dictionary learning algorithm and its application to 3-D medical image denoising. IEEE Trans Biomed Eng 59(2):417–427
Li Z, Yu L, Trzasko JD, Lake DS, Blezek DJ, Fletcher JG, McCollough CH, Manduca A (2014) Adaptive nonlocal means filtering based on local noise level for CT denoising. Med Phys 41(1):011908
Liu B, Yu H, Verbridge SS, Sun L, Wang G (2014) Dictionary-learning-based reconstruction method for electron tomography. Scanning 36(4):377–383
Lou Y, Zhang X, Osher S, Bertozzi A (2010) Image recovery via nonlocal operators. J Sci Comput 42(2):185–197
Lu Y, Zhao J, Wang G (2012) Few-view image reconstruction with dual dictionaries. Phys Med Biol 57(1):173
Ma J, Huang J, Feng Q, Zhang H, Lu H, Liang Z, Chen W (2011) Low-dose computed tomography image restoration using previous normal-dose scan. Med Phys 38(10):5713–5731
Ma J, Zhang H, Gao Y, Huang J, Liang Z, Feng Q, Chen W (2012) Iterative image reconstruction for cerebral perfusion CT using a pre-contrast scan induced edge-preserving prior. Phys Med Biol 57(22):7519
Maggioni M, Katkovnik V, Egiazarian K, Foi A (2013) A nonlocal transform-domain filter for volumetric data denoising and reconstruction. IEEE Trans Image Process 22(1):1057–7149
Mairal J, Bach F, Ponce J (2012) Task-driven dictionary learning. IEEE Trans Pattern Anal Mach Intell (PAMI) 34(4):791–804
Mairal J, Bach F, Ponce J (2014) Sparse modeling for image and vision processing. Found Trends Comput Graph Vis 8(2–3):85–283
Mairal J, Bach F, Ponce J, Sapiro G (2010) Online learning for matrix factorization and sparse coding. J Mach Learn Res (JMLR) 11:19–60
Mairal J, Bach F, Ponce J, Sapiro G, Zisserman A (2009) Non-local sparse models for image restoration. In: International conference on computer vision (ICCV). I
Mairal J, Sapiro G, Elad M (2008) Learning multiscale sparse representations for image and video restoration. Multiscale Model Simul 7(1):214–241
Peyr G, Bougleux S, Cohen L (2008) Non-local regularization of inverse problems. In: Forsyth D, Torr P, Zisserman A (eds) Computer vision ECCV 2008, vol 5304, Lecture notes in computer ScienceSpringer, Berlin, pp 57–68
Pfister L, Bresler Y (2014) Model-based iterative tomographic reconstruction with adaptive sparsifying transforms . In: IS&T/SPIE electronic imaging, International Society for Optics and Photonics, pp 90200H–90200H
Protter M, Elad M, Takeda H, Milanfar P (2009) Generalizing the nonlocal-means to super-resolution reconstruction. IEEE Trans Image Process 18(1):36–51
Ramirez I, Sprechmann P, Sapiro G (June 2010) Classification and clustering via dictionary learning with structured incoherence and shared features. In: 2010 IEEE conference on computer vision and pattern recognition (CVPR), pp 3501–3508
Rubinstein R, Zibulevsky M, Elad M (2010) Double sparsity: learning sparse dictionaries for sparse signal approximation. IEEE Trans Signal Process 58(3):1553–1564
Sakhaee E, Entezari A (2014) Learning splines for sparse tomographic reconstruction. In: Bebis G, Boyle R, Parvin B, Koracin D, McMahan R, Jerald J, Zhang H, Drucker S, Kambhamettu C, El Choubassi M, Deng Z, Carlson M (eds) Advances in visual computing, vol 8887. Lecture notes in computer science. Springer International Publishing, pp 1–10
Salmon J, Harmany Z, Deledalle C-A, Willett R (2014) Poisson noise reduction with non-local PCA. J Math Imaging Vis 48(2):279–294
Shtok J, Elad M, Zibulevsky M (2013) Learned shrinkage approach for low-dose reconstruction in computed tomography. J Biomed Imaging 2013:7
Shtok J, Elad P, Zibulevsky M (May 2011) Sparsity-based sinogram denoising for low-dose computed tomography. In: 2011 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 569–572
Soltani S (2015) Studies of sensitivity in the dictionary learning approach to computed tomography: simplifying the reconstruction problem, rotation, and scale. DTU Compute-Technical Report-2015. Technical University of Denmark
Soltani S, Andersen MS, Hansen PC (2015) Tomographic image reconstruction using dictionary priors. CoRR, abs/1503.01993
Stojanovic I, Pien H, Do S, Karl W (May 2012) Low-dose X-ray CT reconstruction based on joint sinogram smoothing and learned dictionary-based representation. In: 2012 9th IEEE international symposium on biomedical imaging (ISBI), pp 1012–1015
Tan S, Zhang Y, Wang G, Mou X, Cao G, Wu Z, Yu H (2015) Tensor-based dictionary learning for dynamic tomographic reconstruction. Phys Med Biol 60(7):2803
Tian Z, Jia X, Dong B, Lou Y, Jiang SB (2011) Low-dose 4DCT reconstruction via temporal nonlocal means. Med Phys 38(3):1359–1365
Wang S, Zhang L, Liang Y, Pan Q (2012) Semi-coupled dictionary learning with applications to image super-resolution and photo-sketch synthesis. In 2012 IEEE conference on computer vision and pattern recognition (CVPR), IEEE, pp 2216–2223
Xu Q, Yu H, Mou X, Zhang L, Hsieh J, Wang G (2012) Low-dose X-ray CT reconstruction via dictionary learning. IEEE Trans Med Imaging 31(9):1682–1697
Xu W, Ha S, Mueller K (2013) Database-assisted low-dose CT image restoration. Med Phys 40(3):031109
Xu W, Mueller K (2012) Efficient low-dose CT artifact mitigation using an artifact-matched prior scan. Med Phys 39(8):4748–4760
Yan H, Zhen X, Cervio L, Jiang SB, Jia X (2013) Progressive cone beam CT dose control in image-guided radiation therapy. Med Phys 40(6):060701
Yang J, Wright J, Huang T, Ma Y (2010) Image super-resolution via sparse representation. IEEE Trans Image Process 19(11):2861–2873
Zhang H, Huang J, Ma J, Bian Z, Feng Q, Lu H, Liang Z, Chen W (2014) Iterative reconstruction for X-ray computed tomography using prior-image induced nonlocal regularization. IEEE Trans Biomed Eng 61(9):2367–2378
Zhang H, Ma J, Wang J, Liu Y, Lu H, Liang Z (2014) Statistical image reconstruction for low-dose CT using nonlocal means-based regularization. Comput Med Imaging Graph 38(6):423–435
Zhang X, Burger M, Bresson X, Osher S (2010) Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. SIAM J Imaging Sci 3(3):253–276
Zhao B, Ding H, Lu Y, Wang G, Zhao J, Molloi S (2012) Dual-dictionary learning-based iterative image reconstruction for spectral computed tomography application. Phys Med Biol 57(24):8217
Zhou M, Chen H, Paisley J, Ren L, Sapiro G, Carin L (2009) Non-parametric Bayesian dictionary learning for sparse image representations 1. In: NIPS 2009
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent
This articles does not contain patient data.
Rights and permissions
About this article
Cite this article
Karimi, D., Ward, R.K. Patch-based models and algorithms for image processing: a review of the basic principles and methods, and their application in computed tomography. Int J CARS 11, 1765–1777 (2016). https://doi.org/10.1007/s11548-016-1434-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11548-016-1434-z