Kernel Methods and its Application in Wavefront Reconstruction

Abstract:

Kernel methods can effectively deal with the nonlinear problem. The methods not only can be used for data de-noising, also be effective for classification problems. Using kernel PCA method, we provide a more precise Zernike expansion, which can apparently improve the reconstruction accuracy. At the same time, explore learning the kernel function by the alignment. We verify that the alignment value and recognition rate is proportional relationship.

• Periodical: Advanced Materials Research (Volumes 756-759)
• Pages: 3596-3601
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.756-759.3596
• Online since: September 2013
• Authors: Zhi Ying Tan, Ying Chen, Kun She, Yong Feng
• Keywords: Adaptive Optics, Alignment, Kernel Pca, Zernike Polynomials

References

[1] Z. Ghahramani, Unsupervised learning. Adv. Lect. Machine Learning, 72 (2004).

[2] L. K. Saul and S. T. Roweis, Think globally, fit locally: unsupervised learning of low dimensional manifolds. J. Mach. Learn. Res. 4, 119 (2003).

[3] N. Cristianini, J. Shawe-Taylor, Elisseeff A, et al. On kernel-target alignment [J]. In Advances in Neural Information Processing Systems (NIPS). 2002, 14: 367–373.

[4] C. Cortes, M. Mohri, A. Roatamizadeh. Two-stage learning kernel algorithms. Proc. of the 27th IICML (2010).

[5] H. Saigo, J. P. Vert, et al. Protein homology detection using string alignment kernels. Bioinformatics, 2004, 20(11): 1682-1689.

DOI: 10.1093/bioinformatics/bth141

[6] S. Mika, B. Schölkophf, A. Smola, K. -R. Müller, M. Scholz, and G. Rätsch. Kernel PCA and de-noising in feature spaces. In Advances in Neural Information Processing Systems 11, 1999. 783-789.

[7] R. K. Tyson. Adaptive optics engineering handbook. (CRC Press 1999).

[8] A. Vyas, M. B. Roopashree, B. R. Prasad. Extrapolating Zernike Moments to Predict Future Optical Wave-fronts in Adaptive Optics Using Real Time Data Mining, (2010).

[9] H. E. Rushmeier, K. E. Torrance. The zonal method for calculating light intensities in the presence of a participating (1987).

DOI: 10.1145/37402.37436

[10] G. M. Dai. Modal wave-front reconstruction with Zernike polynomials and Karhunen-Loève functions. (1996).

DOI: 10.1364/josaa.13.001218

[11] W. H. Jiang, H. G. Li. Hartmann-Shack wavefront sensing and wavefront control algorithm. SPIE, 1271: 8293( 1990).

[12] M. Stangalini, D. D. Moro, F. Berrilli, O. Lühe. Zernike basis optimization for solar adaptive optics by using information theory. (2010).

DOI: 10.1364/ao.49.002090

[13] R. J. Noll. Zernike polynomials and atmospheric turbulence. (1976).

[14] B. Schölkopf, A. Smola, K. R. Müller. Nonlinear component analysisas a kernel eigenvalue problem. (1998).

[15] S. Saitoh. Theory of reproducing Kernels and its Applications. Longman Scientific & Technical, Harlow, England (1988).

[16] B. Schölkopf. Support vector learning. Oldenbourg Verlag, Munich, (1997).