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I Have been working in wavelet and shearlet analysis for the past couple of months. However I am working in the analysis side rather than the numerics side. In my work I have been considering the geometry of the shearlet coefficients due to the scaling, shearing and translation. However I have found that the scaling and shearing both affect the overall size of the shearlet domain.

I have been told that there exists a transform that utilizes a rotation matrix rather than a shearing matrix to control the orientation of the analysing functions. However when looking online I can't find such a transform. Does such a transform actually exist and if it does what is it called?

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You are probably looking for curvelets (or ridgelets). They are well suited for approximating functions with jump across smooth curves but don't have a group structure like wavelets or shearlets.

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  • $\begingroup$ Yep!! They look like exactly what I need. Thank you!! $\endgroup$ Oct 9, 2019 at 3:36

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