Continuous curvelet transform

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Transforms and Operators for Directional Bioimage Analysis: A Survey. (2016, background): “The reason for computing the rate of decay of the coefficients is their connection to the local regularity: the faster the decay rate, the smoother the image at location b and orientation θ (see [10, 37, 57]).”
Sparsity- and continuity-promoting seismic image recovery with curvelet frames (2008, background): “Curvelet frames, on the other hand, are designed to detect the wavefront set [6, 8 ,9,11] and lead, as shown in Fig. 6, to better empirical compression rates for real and synthetic seismic images.”
Resolution of the wavefront set using continuous shearlets (2006, background): “In particular, the Continuous Curvelet Transform of Candès and Donoho is closely related to the successful discrete curvelet construction [5].”
The curvelet representation of wave propagators is optimally sparse (2004, background): “Curvelets are ideal for representing wavefront phenomena [ 8 ], or objects which display curve-punctuated smoothness —smoothness except for discontinuity along a general curve with bounded curvature [6, 7]. This fact originally motivated their construction [6, 7]. For example, [7] established that c”
A Shearlet Approach to Edge Analysis and Detection (2009, unknown): “The shearlet transform has similarities to the curvelet transform, first introduced by Candès and Donoho [10], [22].”