Directional multiresolution image representations

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Fast Discrete Curvelet Transforms (2006, positive): “Given the significance of such intermediate dimensional phenomena, there has been a vigorous research effort to provide better adapted alternatives by combining ideas from geometry with ideas from traditional multiscale analysis [17, 19, 4, 31, 14, 16].”
Directionlets: anisotropic multidirectional representation with separable filtering (2006, methodology): “Multi-directionality has also been exploited in bandelets [64; 65; 66], edgelets and wedgelets [31; 74; 75; 107; 108], curvelets [9; 10; 11], and contourlets [27; 28].”
New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities (2004, methodology): “Finally, we recently became aware of the work of Do and Vetterli on contourlets [13, 14], which is also directly inspired by the curvelet transform.”
Directional multiscale modeling of images using the contourlet transform (2006, background): “This is because the basis functions corresponding to the vertical and horizontal subbands are defined over different sampling lattices [21].”