Communications - Scientific Letters of the University of Zilina 2013, 15(11):174-179 | DOI: 10.26552/com.C.2013.2A.174-179
Image Extrapolation Using Sparse Methods
- 1 Department of Telecommunications, Brno University of Technology, Brno, Czech Republic
Image extrapolation is the specific application in image processing. You have to extrapolate the image for example when you want to process the given image piecewise. When the border patches are incompleted you must extrapolate them to the given size. Nowadays,some basic extrapolations, e.g. linear, polynomial etc. are used. The advanced methods are presented in this paper. We are using the algorithms that are based on finding the sparse solutions in underdetermined systems of linear equations. Three algorithms are presented for image extrapolation. First one is the K-SVD algorithm. K-SVD is the algorithm that trains a dictionary which allows the optimal sparse representation. Second one is Morphological Component Analysis (MCA) which is based on Independent Component Analysis (ICA). The last is the Expectation Maximization (EM) algorithm. This algorithm is statistics-based. These three algorithms for image extrapolation are compared on the real images.
Keywords: image extrapolation, sparse, K-SVD, MCA, EM
Published: July 31, 2013 Show citation
References
- SIMAK, B., KARPF, M.: Salt & Pepper Noise Impact on Image Coding Based on Image Splitting, Communications - Scientific Letters of the University of Zilina, vol. 2, pp. 16-20, 2000.
Go to original source... - ELAD, M., AHARON, M.: Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries, Image Processing, IEEE Transactions on, vol. 15, no. 12, pp. 3736-3745, dec. 2006. Go to original source...
- ELAD, M.: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, Springer, 2010. Go to original source...
- ZHANG, H., ZHANG, Y.: Sparse Representation Based Iterative Incremental Image Deblurring, in Proceedings of the 16th IEEE intern. conference on Image processing, Piscataway, 2009, ICIP'09, pp. 1285-1288, IEEE Press.
- FADILI, M. J., STARCK, J. L., MURTAGH, F.: Inpainting and Zooming Using Sparse Representations, The Computer Journal, 2007. Go to original source...
- SPIRIK, J.: Algorithms for Computing Sparse Solutions, in Proc. of the 17th conference STUDENT EEICT vol. 3, 2011, pp. 123-127.
- AHARON, M., ELAD, M., BRUCKSTEIN, A. M.: K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representations, IEEE Transactions on Signal Processing, vol. 54, pp. 4311-4322, 2006. Go to original source...
- STARCK, J. L., ELAD, M., DONOHO, D. L.: Redundant Multiscale Transforms and Their Application for Morphological Component Analysis, Advances in Imaging and Electron Physics, vol. 132, 2004. Go to original source...
- ELAD, M., STARCK, J. L., QUERRE P., DONOHO, D. L.: Simultaneous Cartoon and Texture Image Inpainting Using Morphological Component Analysis (MCA), Applied and Computational Harmonic Analysis, vol. 19, no. 3, pp. 340-358, 2005. Go to original source...
- CANDES, E., DEMANET, L., DONOHO, D. L., YING, L.: Fast Discrete Curvelet Transforms, Multiscla Modeling & Simulation, vol. 5, no. 3, pp. 861-899, 2006. Go to original source...
- GYAOUROVA, A., KAMATH, CH., FODOR, I. K.: Undecimated Wavelet Transforms for Image De-Noising, Tech. Rep., 2002. Go to original source...
This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.