Shearlet Smoothness Spaces
نویسندگان
چکیده
The shearlet representation has gained increasingly more prominence in recent years as a flexible mathematical framework which enables the efficient analysis of anisotropic phenomena by combining multiscale analysis with the ability to handle directional information. In this paper, we introduce a class of shearlet smoothness spaces which is derived from the theory of decomposition spaces recently developed by L. Borup and M. Nielsen. The introduction of these spaces is motivated by recent results in image processing showing the advantage of using smoothness spaces associated with directional multiscale representations for the design and performance analysis of improved image restoration algorithms. In particular, we examine the relationship of the shearlet smoothness spaces with respect to Besov spaces, curvelet-type decomposition spaces and shearlet coorbit spaces. With respect to the theory of shearlet coorbit space, the construction of shearlet smoothness spaces presented in this paper does not require the use of a group structure.
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