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Linear transforms and expansions are fundamental mathematical tools of signal processing. Accordingly, wavelet transform has played an important role in several signal processing tasks such as compression and denoising. However, wavelet transform fails to represent effectively the images, which have edges and treated them as smooth functions with discontinuities along curves. The curvelet transform has been developed as an alternative to wavelet transform in which frame elements are indexed by scale, location, and orientation parameters. The elements obey a special scaling law, where the length of the support of frame elements is approximately equal to square of the width of the support. Recently it has an important impact in image processing and communications.