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7. Conclusion
A digital implementation of the curvelet transform was proposed and applied on two
images: a synthetic image (where the distribution of the noise is known) and a real image
(where the distribution of the noise is not known). The resuits are promising on both the
synthetic image and the real image. They show significant reduction of the noise while
preserving the edges of the image.
While the results are promising there is much work to be done. In the denoising scheme
the threshold is chosen with ad hoc methods. A great improvement would be made by
finding some criteria for choosing this threshold.
References
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[5] J. Starck, EJ. Candes, and D.L. Donoho. The curvelet transform for image denoising. Technical Report, Department of
Statistics, Stanford University, 1998.
[6] E J. Candes, Ridgelets. Theory and Applications. Ph.D. thesis, Stanford University, 1998.
[7] D.L. Donoho and M.R. Duncan. Digital curvelet transform: Strategy, implementation and experiments. Technical Report,
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[8] A. Averbuch, RR. Coifman, D.L. Donoho, M. Israeli, and J. Walden. Fast Slant Stack:A notion ofRadon transform for data
in a cartesian grid which is rapidly computable, algebraically exact, geometrically faithful and invertible. To appear in
SIAM Journal of Scientific Computing, 2001.
[9] D.L. Donoho and A.G. Flesia. Digital ridgelet transform based on true ridge functions. Technical Report, Department of
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[10] J.S. Lee. Digital image enhancement and noise filtering by use oflocalstatistics. IEEE Trans. Pattern Anal. Machine Intell,
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Arbók VFÍ/TFÍ 2002