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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 23 — Aug. 10, 2002
  • pp: 4806–4811

Digital restoration of defocused images in the wavelet domain

Edmund Y. Lam  »View Author Affiliations


Applied Optics, Vol. 41, Issue 23, pp. 4806-4811 (2002)
http://dx.doi.org/10.1364/AO.41.004806


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Abstract

Many cameras nowadays are equipped with an autofocus mechanism that attempts to take pictures at the best possible focus. However, there are situations in which the pictures are still out of focus, such as when the photographer has mistakenly focused at a wrong position or when the focusing region consists of objects of different depths and therefore confuses the autofocus system. With a digital camera, we can attempt to use digital image-restoration techniques to bring the pictures back into focus. We design an algorithm that restores the image by digitally enhancing the corresponding frequency bands. We employ the restoration in the wavelet domain so that this restoration scheme can be compliant with JPEG 2000, which is positioned to succeed JPEG as the next image-compression standard and has the potential to be widely adopted by the digital photography industry owing to its many advanced features.

© 2002 Optical Society of America

OCIS Codes
(100.3020) Image processing : Image reconstruction-restoration
(100.7410) Image processing : Wavelets
(110.5200) Imaging systems : Photography
(220.1000) Optical design and fabrication : Aberration compensation
(220.2560) Optical design and fabrication : Propagating methods

History
Original Manuscript: June 4, 2001
Revised Manuscript: April 29, 2002
Published: August 10, 2002

Citation
Edmund Y. Lam, "Digital restoration of defocused images in the wavelet domain," Appl. Opt. 41, 4806-4811 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-23-4806


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References

  1. W. Pennebaker, J. Mitchell, JPEG Still Image Data Compression Standard (Van Nostrand Reinhold, New York, 1992).
  2. D. Taubman, M. Marcellin, JPEG2000: Image Compression Fundamentals, Standards, and Practice (Kluwer Academic, Boston, 2001).
  3. E. Y. Lam, P. Y. Tam, X. Ouyang, “An efficient parallel implementation of the 2-D pyramidal discrete wavelet transform,” in 2001 International Conference on Imaging Science, Systems, and Technology (CSREA Press, Las Vegas, Nev., 2001), Vol. 1, pp. 178–183.
  4. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  5. E. Y. Lam, J. W. Goodman, “Discrete cosine transform domain restoration of defocused images,” Appl. Opt. 37, 6213–6218 (1998). [CrossRef]
  6. M. Vetterli, J. Kovac̆ević, Wavelets and Subband Coding (Prentice Hall, Englewood Cliffs, N. J., 1995).
  7. G. Strang, T. Nguyen, Wavelets and Filter Banks (Wellesley-Cambridge, Wellesley, Mass., 1996).
  8. S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989). [CrossRef]
  9. E. Y. Lam, J. W. Goodman, “A mathematical analysis of the DCT coefficient distributions for images,” IEEE Trans. Image Process. 9, 1661–1666 (2000). [CrossRef]
  10. K. Panchapakesan, A. Bilgin, M. W. Marcellin, B. R. Hunt, “Joint compression and restoration of images using wavelets and non-linear interpolative vector quantization,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1998), Vol. 5, pp. 2649–2652.
  11. A. Gersho, R. Gray, Vector Quantization and Signal Compression (Kluwer Academic, Boston, 1992). [CrossRef]
  12. E. Y. Lam, “Image restoration algorithms for monochrome digital photography,” Ph.D. dissertation, (Stanford University, Stanford, Calif., 2000).

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