Abstract
The relative Newton algorithm, previously proposed for quasi maximum likelihood blind source separation and blind deconvolution of one-dimensional signals is generalized for blind deconvolution of images. Smooth approximation of the absolute value is used in modelling the log probability density function, which is suitable for sparse sources. We propose a method of sparsification, which allows blind deconvolution of sources with arbitrary distribution, and show how to find optimal sparsifying transformations by training.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chan, T.F., Wong, C.K.: Total variation blind deconvolution (IEEE. Trans. Image Proc.) (to appear)
Kaftory, R., Sochen, N.A., Zeevi, Y.Y.: Color image denoising and blind deconvolusion using the beltramy operator. In: Proc. 3rd Intl. Symposium on Image and Sig. Proc. and Anal., pp. 1–4 (2003)
Zibulevsky, M.: Sparse source separation with relative Newton method. In: Proc. ICA 2003, pp. 897–902 (2003)
Bronstein, A.M., Bronstein, M., Zibulevsky, M.: Blind deconvolution with relative Newton method. Technical Report 444, Technion, Israel (2003)
Amari, S.I., Cichocki, A., Yang, H.H.: Novel online adaptive learning algorithms for blind deconvolution using the natural gradient approach. In: Proc. SYSID, pp. 1057–1062 (1997)
Pham, D., Garrat, P.: Blind separation of a mixture of independent sources through a quasimaximum likelihood approach. IEEE Trans. Sig. Proc. 45, 1712–1725 (1997)
Kisilev, P., Zibulevsky, M., Zeevi, Y.: Multiscale framework for blind source separation. JMLR (2003) (in press)
Zibulevsky, M., Pearlmutter, B.A.: Blind source separation by sparse decomposition. Neural Computation 13 (2001)
Zibulevsky, M., Kisilev, P., Zeevi, Y.Y., Pearlmutter, B.A.: Blind source separation via multinode sparse representation. In: Proc. NIPS (2002)
Bronstein, A.M., Bronstein, M., Zeevi, Y.Y., Zibulevsky, M.: Quasi-maximum likelihood blind deconvolution of images using sparse representations. Technical report, Technion, Israel (2003)
Lewicki, M.S., Olshausen, B.A.: A probabilistic framework for the adaptation and comparison of image codes. J. Opt. Soc. Am. A 16, 1587–1601 (1999)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)
Blomgren, P., Chan, T.F., Mulet, P., Wong, C.: Total variation image restoration: numerical methods and extensons. In: Proc. IEEE ICIP (1997)
Chan, T.F., Mulet, P.: Iterative methods for total variation image restoration. SIAM J. Num. Anal. 36 (1999)
Moscoso, M., Keller, J.B., Papanicolaou, G.: Depolarization and blurring of optical images by biological tissue. J. Opt. Soc. Am. A 18, 948–960 (2001)
Banham, M.R., Katsaggelos, A.K.: Spatially adaptive wavelet-based multiscale image restoration. IEEE Trans. Image Processing 5, 619–634 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bronstein, A.M., Bronstein, M.M., Zibulevsky, M., Zeevi, Y.Y. (2004). Optimal Sparse Representations for Blind Deconvolution of Images. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_64
Download citation
DOI: https://doi.org/10.1007/978-3-540-30110-3_64
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23056-4
Online ISBN: 978-3-540-30110-3
eBook Packages: Springer Book Archive