Abstract
We propose a method for solving linear space-time variant blind source separation (BSS) problem with additive noise, x=As+n, on the “pixel-by-pixel” basis i.e. assuming that unknown mixing matrix is different for every space or time location. Solution corresponds with the isothermal-To equilibrium of the free energy H =U-ToS contrast function where U represents the input/output energy exchange and S represents the Shannon entropy. Solution of the inhomogeneous equation (data model with additive noise) is obtained by augmenting inhomogeneous equation into homogeneous “noise free” equation. Consequently, data model with additive noise can be solved by algorithm for the noise free space-time variant BSS problems, [1],[2]. We demonstrate the algorithm capability to perfectly recover images from the space variant mixture of two images with additive noise.
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.
References
Szu, H., Kopriva, I.: Unsupervised Learning with Stochastic Gradient (submitted to Neurocomputing)
Szu, H., Kopriva, I.: Deterministic Blind Source Separation for Space Variant Imaging. In: Amari, S.I., Cichocki, A., Makino, S., Murata, N. (eds.) Proc. of the Fourth International Symposium on Independent Component Analysis and Blind Signal Separation, Nara, Japan, April 1-4, pp. 669–674 (2003)
Szu, H.H., Hsu, C.: Landsat spectral Unmixing à la superresolution of blind matrix inversion by constraint MaxEnt neural nets. In: Proc. SPIE 3078, pp. 147–160 (1997)
Szu, H., Kopriva, I.: Comparison of the Lagrange Constrained Neural Network with Traditional ICA Methods. In: Proc. of the IEEE 2002 World Congress on Computational Intelligence- International Joint Conference on Neural Networks, Hawaii, USA, May 17-22, pp. 466–471 (2002)
Amari, S., Cihocki, A., Yang, H.H.: A new learning algorithm for blind signal separation. In: Advances in Neural Information Processing Systems, vol. 8, pp. 757–763. MIT Press, Cambridge (1996)
Bell, A.J., Sejnowski, T.J.: An information-maximization approach to blind separation and blind deconvolution. Neural Comp. 7, 1129–1159 (1995)
Hyvärinen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Computation 9, 1483–1492 (1997)
Cardoso, J.F., Soulomniac, A.: Blind beamforming for non-Gaussian signals. Proc. IEE F 140, 362–370 (1993)
Plumbley, M.: Algorithms for Nonnegative Independent Component Analysis. IEEE Transaction on Neural Networks 14(3), 534–543 (2003)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(21), 788–791 (1999)
Parra, L., Spence, C., Sajda, P., Ziehe, A., Müller, K.-R.: Unmixing Hyperspectral Data. In: Jolla, S.A., Leen, T.K., Müller, K.-R. (eds.) Advances in Neural Information Processing Systems (NIPS12), MIT Press, Cambridge (2000)
Huang, K.: Statistical Mechanics. J. Wiley, Chichester (1963)
Szu, H.H., Kopriva, I.: Artificial Neural Networks for Noisy Image Super-resolution. Optics Communications 198(1-3), 71–81 (2001)
Szu, H., Hartley, R.: Fast Simulated Annealing. Physical Letters A 122(3), 157–162 (1987)
Szu, H., Kopriva, I.: Cauchy Machine for Blind Inversion in Linear Space-Variant Imaging. In: Proc. of the 2003 IEEE International Joint Conference on Neural Networks, Portland, OR, July 20-24, vol. I, pp. 747–752 (2003)
Kopriva, I., Du, Q., Szu, H., Wasylkiwskyj, W.: Independent Component Analysis Approach to Image Sharpening in the Presence of Atmospheric Turbulence. Optics Communications 233(1-3), 7–14 (2004)
Chandrasekhar, S.: Stochastic Problems in Physics and Astronomy. Review of Modern Physics 15(1), 1–87 (1943)
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
Kopriva, I., Szu, H. (2004). Space-Time Variant Blind Source Separation with Additive Noise. 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_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-30110-3_31
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