IMAGE COMPLETION WITH LOW-RANK MODEL APPROXIMATION METHODS
Tomasz Sadowski
tomasz.sadowski@pwr.edu.plPolitechnika Wrocławska, Wydział Elektroniki (Poland)
Rafał Zdunek
Politechnika Wrocławska, Wydział Elektroniki (Poland)
Abstract
The paper is concerned with the task of reconstructing missing pixels in images perturbed with impulse noise in a transmission channel. Such a task can be formulated in the context of image interpolation on an irregular grid or by approximating an incomplete image by low-rank factor decomposition models. We compared four algorithms that are based on the low-rank decomposition model: SVT, SmNMF-MC , FCSA-TC and SPC-QV. The numerical experiments are carried out for various cases of incomplete images, obtained by removing random pixels or regular grid lines from test images. The best performance is obtained if nonnegativity and smoothing constraints are imposed onto the estimated low-rank factors.
Keywords:
image completion, low-rank approximation, nonnegative matrix factorization, tensor decomposition, matrix completionReferences
Ashikhmin M.: Synthesizing natural textures. I3D'01 Proceedings of the 2001 symposium on Interactive 3D graphics, 217–226, [doi: 10.1145/364338.364405].
Google Scholar
Ballester C., Bertalm M., Caselles V., Sapiro G., Verdera .: Filling-in by joint interpolation of vector fields and gray levels. IEEE Transactions on Image Processing 8/2001, 1200–1211, [doi: 10.1109/83.935036].
Google Scholar
Beck A., Teboulle M.: Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems. IEEE Trans. Image Process. 11/2009, [doi: 10.1109/TIP.2009.2028250].
Google Scholar
Bertalmio M., Sapiro G., Caselles V., Ballester C.: Image inpainting. SIGGRAPH'00 Proceedings of the 27th annual conference on Computer graphics and interactive techniques, 2000, 417–424, [doi: 10.1145/344779.344972].
Google Scholar
Bertalmio M., Bertozzi A., Sapiro G.: Navier-Stokes, fluid dynamics, and image and video inpainting. CVPR 1, 2001, 355–362, [doi: 10.1109/CVPR.2001.990497].
Google Scholar
Bertalmio M., Vese L., Sapiro G., Osher S.: Simultaneous structure and texture image inpainting. CVPR 8, 2003, 707–712, [doi: 10.1109/TIP.2003.815261].
Google Scholar
Bonet J.: Multiresolution sampling procedure for analysis and synthesis of texture images. Computer Graphics, Annual Conference Series, 1997, 361–368, [doi: 10.1145/258734.258882].
Google Scholar
Cai J.-F., Candes E., Shen Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim 4/2010, 1956–1982, [doi: 10.1137/080738970].
Google Scholar
Chan T., Shen J.: Non-texture inpaintings by curvature-driven diffusions. J. Visual Comm. Image Rep. 4/2001, 436–449, [doi: 10.1006/jvci.2001.0487].
Google Scholar
Chen Y-L., Hsu C.-T., Liao H.-Y.: Simultaneous tensor decomposition and completion using factor priors. IEEE Transactions on Pattern Analysis and Machine Intelligence 3/2014, 577–591, [doi: 10.1109/TPAMI.2013.164].
Google Scholar
Cichocki A., Zdunek R., Phan A., Amari S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley and Sons, Chichester 2009.
Google Scholar
Efros A., Leung T.: Texture synthesis by non-parametric sampling. Proc. IEEE Int. Conf. Comput. Vis., 1999, 1033–1038, [doi: 10.1109/ICCV.1999.790383].
Google Scholar
Gandy S., Recht B., Yamada I.: Tensor completion and low-n-rank tensor recovery via convex optimization. Inverse Problems 27, 2011, 025010, [doi: 10.1088/0266-5611/27/2/025010].
Google Scholar
Guo X., Ma Y.: Generalized Tensor Total Variation Minimization for Visual Data Recovery. IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2015, 3603–3611, [doi: 10.1109/CVPR.2015.7298983].
Google Scholar
Han X., Wu J., Wang L., Chen Y.,Senhadji L., Shu H.: Linear Total Variation Approximate Regularized Nuclear Norm Optimization for Matrix Completion. Abstract & Applied Analysis 2014, 765782, [doi: 10.1155/2014/765782].
Google Scholar
Heeger D., Bergen J.: Pyramid-based texture analysis/synthesis. SIGGRAPH'95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, 229–238, [doi: 10.1145/218380.218446].
Google Scholar
Herman G.: Fundamentals of computerized tomography: Image reconstruction from projection (2nd edition). Springer, New York 2009.
Google Scholar
Hertzmann A., Jacobs C., Oliver N., Curless B., Salesin D.: Image analogies. SIGGRAPH '01 Proceedings of the 28th annual conference on Computer graphics and interactive techniques, 327–340, [doi: 10.1145/383259.383295].
Google Scholar
Huang J., Zhang, S., Dimitris Metaxas D.: Fast Optimization for Mixture Prior Models. Computer Vision – ECCV 2010. ECCV 2010. Lecture Notes in Computer Science 6313, 2010, 607–620, [doi: 10.1007/978-3-642-15558-1_44].
Google Scholar
Ji H., Liu C., Shen Z., Xu Y.: Robust video denoising using low rank matrix completion. Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2010, 1791–1798, [doi: 10.1109/CVPR.2010.5539849].
Google Scholar
Komodakis N., Tziritas G.: Image completion using global optimization. CVPR 2006, 442–452, [doi: 10.1109/CVPR.2006.141 ].
Google Scholar
Kwatra V., Schödl A., Essa I., Turk G., Bobick A.: Graphcut textures: Image and video synthesis using graph cuts. SIGGRAPH 2003, 277–286, [doi: 10.1145/1201775.882264].
Google Scholar
Levin A., Zomet A., Weiss Y.: Learning how to inpaint from global image statistics. Proc. 9th IEEE Int. Conf. Comput. Vis. 2003, 305–312, [doi: 10.1109/ICCV.2003.1238360].
Google Scholar
Li W., Zhao L., Lin Z., Xu D., Lu D.: Non-local image inpainting using low-rank matrix completion. Computer Graphics Forum 2014, 111–122, [doi: 10.1111/cgf.12521].
Google Scholar
Liang L., Liu C., Xu Y., Guo B., Shum H.: Real-time texture synthesis by patch-based sampling. ACM Tran. Graph. 3/2001, 127–150, [doi: 10.1145/501786.501787].
Google Scholar
Liu J., Musialski P., Wonka P., Ye J.: Tensor completion for estimating missing values in visual data. IEEE Transactions on Pattern Analysis and Machine Intelligence 1/2013, 208–220, [doi: 10.1145/501786.501787]
Google Scholar
Phan A., Cichocki A., Tichavsky P., Luta G., Brockmeier A.: Tensor Completion Through Multiple Kronecker Product Decomposition. ICASSP, 2013, 3233–3237, [doi: 10.1109/ICASSP.2013.6638255].
Google Scholar
Portilla J., Simoncelli E.: A parametric texture model based on joint statistics of complex wavelet coefficients. IJCV, 1/2000, 49–70, [doi: 10.1023/A:1026553619983].
Google Scholar
Roth S., Black M.: Fields of experts: A framework for learning image priors. Proc. IEEE Comput. Vis. Pattern Recog., 2005, 860–867, [doi: 10.1109/CVPR.2005.160].
Google Scholar
Sikora J., Wójtowicz S. (eds): Industrial and Biological Tomography: Theoretical Basis and Applications. Wydawnictwo Książkowe Instytutu Elektrotechniki, Warszawa 2010.
Google Scholar
Troyanskaya O., Cantor M., Sherlock G., Brown P., Hastie T., Tibshirani R., D. Botstein, Altman R.: Missing value estimation methods for DNA microarrays. Bioinformatics 6/2001, 520–525, [doi: 10.1186/1471-2105-7-32].
Google Scholar
Wei L., Levoy M.: Fast texture synthesis using tree-structured vector quantization. SIGGRAPH'00 Proceedings of the 27th annual conference on Computer graphics and interactive techniques, 479–488, [doi: 10.1145/344779.345009].
Google Scholar
Wu Q., Yu Y.: Feature matching and deformation for texture synthesis. ACM Trans. Graph. 3/2004, 364–367, [doi: 10.1145/1186562.1015730].
Google Scholar
Yokota T., Zhao Q., Cichocki A.: Smooth PARAFAC Decomposition for Tensor Completion. IEEE Transactions on Signal Processing 64(20), 2016, 5423–5436, [doi: 10.1109/TSP.2016.2586759].
Google Scholar
Zdunek R.: Nieujemna faktoryzacja macierzy i tensorów: zastosowanie do klasyfikacji i przetwarzania sygnałów. Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław 2014.
Google Scholar
http://perception.csl.illinois.edu/matrix-rank/sample_code.html#MC, [25.04.2016].
Google Scholar
http://ranger.uta.edu/~huang/R_LSI.htm, [25.04.2016].
Google Scholar
https://sites.google.com/site/yokotatsuya/home/software/smooth-parafac-decomposition-for-tensor-completion, [25.04.2016].
Google Scholar
Authors
Tomasz Sadowskitomasz.sadowski@pwr.edu.pl
Politechnika Wrocławska, Wydział Elektroniki Poland
Authors
Rafał ZdunekPolitechnika Wrocławska, Wydział Elektroniki Poland
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