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Alternating Projection onto Convex Sets

Resources

Chapter 11 in

Handbook of Fourier Analysis & Its Applications

has the most complete treatment of POCS of which we are aware. Available in print (left) or in electronic form (right).

For more information about this book, visit its web site:

http://www.HandbookOfFourierAnalysis.com/


Other resources

POCS Power Point Presentation

This POCS presentation contains a number of video clips. To download a zip file including both the power point presentation and the video clips, click HERE.

TUTORIAL: R.J. Marks II, "Alternating Projections onto Convex Sets", in Deconvolution of Images and Spectra, edited by Peter A. Jansson, (Academic Press, San Diego, 1997), pp.476-501 (pdf)

DEMO: Scott Philips, "Reconstruction of a Speech Signal Using Projections on Convex Surfaces" with audio examples (html)

 

 

CIA POCS Publications.

To download pdf files of these papers, visit Robert Marks's publication page.

M.H. Goldburg and R.J. Marks II, "Signal synthesis in the presence of an inconsistent set of constraints", IEEE Transactions on Circuits and Systems, vol. CAS-32 pp. 647-663 (1985).R.J. Marks II, "A class of continuous level associative memory neural nets", Applied Optics, vol.26, pp.2005-2010, (1987).

R.J. Marks II, L.E. Atlas and K.F. Cheung, "Optical processor architectures for alternating projection neural networks", Optics Letters, vol. 13, pp.533-535 (1988).

R.J. Marks II, S. Oh and L.E. Atlas, "Alternating projection neural networks", IEEE Transactions on Circuits and Systems, vol.36, pp.846-857 (1989).

S. Oh, R.J. Marks II and D. Sarr, "Homogeneous alternating projection neural networks", Neurocomputing, volume 3, pp. 69-95 (1991).

S. Oh. C.Ramon, M.G. Meyer and R.J. Marks II, "Resolution enhancement of biomagnetic images using the method of alternating projections", IEEE Transactions on Biomedical Engineering, vol. 40, no. 4, pp.323-328 (1993).

S.Oh, R.J. Marks II and L.E. Atlas, "Kernel synthesis for generalized time-frequency distributions using the method of alternating projections onto convex sets", IEEE Transactions on Signal Processing, vol. 42, No.7, July 1994, pp.1653-1661.

P.S. Cho, S. Lee, R.J. Marks II, S.Oh, S.G. Sutlief, M.H. Phillips, "Optimization of Intensity Modulated Beams With Volume Constraints Using Two Methods: Cost Function Minimization and Projections Onto Convex Sets", Medical Physics, (Am. Assoc. Phys. Med.), Vol. 25, No.4, pp.435-443 (April 1998).

P.S. Cho & R.J. Marks II, "Hardware-sensitive optimization for intensity modulated radiotherapy", Phys. Med. Biol, 2000 (pp. 429-440) .

R.J. Marks II, L.E. Atlas, S. Oh and J.A. Ritcey, "The performance of convex set projection based neural networks", Neural Information Processing Systems, Dana Z. Anderson, editor, (American Institute of Physics, New York, 1988), pp. 534-543.

R.J. Marks II, L.E. Atlas and K.F. Cheung, "Architectures for a continuous level neural network based on alternating orthogonal projections", Proceedings of O-E/LASE '88 Conference on Neural Network Models for Optical Computing, Los Angeles, January 1988, SPIE volume 882, pp 90-92.

M.E. Aggoune, L.E. Atlas, D.A. Cohn, M.J. Damborg, M.A. El-Sharkawi and R.J. Marks II, "Artificial neural networks for static system security assessment", Proc. 1989 IEEE International Symposium on Circuits and Systems, pp.490-494, 9-11 May 1989, Portland - invited paper.

S. Oh and R.J. Marks II, "Noise sensitivity of projection neural networks", Proc. 1989 IEEE International Symposium on Circuits and Systems, pp.2201-2204, 9-11 May 1989, Portland.

S.Oh, R.J. Marks II, L.E. Atlas and J.W. Pitton, "Kernel synthesis for generalized time-frequency distributions using the method of projection onto convex sets", SPIE Proceedings 1348, Advanced Signal Processing Algorithms, Architectures, and Implementation, F.T. Luk, Editor, pp.197-207, San Diego, July 10-12, 1990.

C.Ramon, S.Oh, M.G. Meyer and R.J. Marks II, "Biomagnetic image reconstruction using the method of alternating projections", Proceedings of the SPIE, vol.1652, 1992.

S. Oh and R.J. Marks II, "Alternating projections onto fuzzy convex sets", Proceedings of the Second IEEE International Conference on Fuzzy Systems (FUZZ-IEEE `93), San Francisco, March 1993, vol.1, pp. 148-155.

R.J. Marks II, Loren Laybourn, Shinhak Lee and Seho Oh, "Fuzzy and extra crisp alternating projection onto convex sets (POCS)", Proceedings of the International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 427-435, Yokohama, Japan, March 20-24, 1995.

Jiho Park, D.C. Park, R.J. Marks II, M.A. El-Sharkawi, "Block Loss Recovery in DCT Image Encoding Using POCS", IEEE International Symposium on Circuits and Systems, Scottsdale, Arizona, May 26-29, 2002, pp.V 245 - V 248.

 

POCS