Fresnelets: New multiresolution wavelet bases for digital holography

IEEE Transactions on Image Processing

Volumn 12, Issue 1, 2003, Pages 29-43

  Liebling, Michael ^a   Blu, Thierry ^a   Unser, Michael ^a  

^a EPFL   (Switzerland)

Author keywords

B splines; Digital holography; Fresnel transform; Fresnelet transform; Fresnelets; Wavelets

Indexed keywords

HOLOGRAMS; IMAGE RECONSTRUCTION; MATHEMATICAL TRANSFORMATIONS; OPTICAL RESOLVING POWER;

DIGITAL HOLOGRAPHY;

HOLOGRAPHY;

EID: 0037238935     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2002.806243     Document Type: Article

References (20)

1. J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett., vol. 11, no. 3, pp. 77-79, Aug. 1967.
2. L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography. New York: Consultants Bureau, 1980.
3. U. Schnars and W. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt., vol. 33, no. 2, pp. 179-181, Jan. 1994.
4. E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett., vol. 24, no. 5, pp. 291-293, Mar. 1999.
5. D. Gabor, "A new microscopic principle," Nature, vol. 161, no. 4098, pp. 777-778, 1948.
6. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. New York: McGraw-Hill, 1996.
7. E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude-contrast and quantitative phase-constrast microscopy by numerical reconstruction of Fresnel off-axis holograms," Appl. Opt., vol. 38, no. 34, pp. 6994-7001, Dec. 1999.
8. G. Strang and T. Nguyen, Wavelets and Filter Banks. Wellesley, MA: Wellesley-Cambridge, 1996.
9. T. Blu and M. Unser, "Quantitative Fourier analysis of approximation techniques: Part II - Wavelets," IEEE Trans. Signal Processing, vol. 47, pp. 2796-2806, Oct. 1999.
10. M. Unser, A. Aldroubi, and M. Eden, "On the asymptotic convergence of B-spline wavelets to Gabor functions," IEEE Trans. Inform. Theory, vol. 38, pp. 864-872, Mar. 1992.
11. D. Gabor, "Theory of communication," J. Inst. Elect. Eng. (London), vol. 93, pp. 429-457, 1946.
12. A. J. E. M. Janssen, "Gabor representation of generalized functions," J. Math. Anal Appl., vol. 83, pp. 377-394, Oct. 1981.
13. M. Unser, "Sampling - 50 years after Shannon," Proc. IEEE, vol. 88, pp. 569-587, Apr. 2000.
14. _, "Splines: A perfect fit for signal and image processing," IEEE Signal Processing Mag., vol. 16, no. 6, pp. 22-38, Nov. 1999.
15. M. Unser and T. Blu, "Fractional splines and wavelets," SIAM Review, vol. 42, no. 1, pp. 43-67, Mar. 2000.
16. M. Unser, A. Aldroubi, and M. Eden, "A family of polynomial spline wavelet transforms," Signal Processing, vol. 30, no. 2, pp. 141-162, Jan. 1993.
17. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. Cambridge, U.K: Cambridge Univ. Press, 1992.
18. T. Kreis, M. Adams, and W. Jüptner, "Methods of digital holography: A comparison," Proc. SPIE, vol. 3098, pp. 224-233, 1997.
19. E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt., vol. 39, no. 23, pp. 4070-4075, Aug. 2000.
20. T. Kreis and W. Jüptner, "Suppression of the DC term in digital holography," Opt. Eng., vol. 36, no. 8, pp. 2357-2360, Aug. 1997.