ABSTRACT
Despite the huge success of wavelets in the domain of image compression, the failure of twodimensionalmultiresolutionwavelets when dealingwith images of the cartoon class, i.e., images consisting of domains of smoothly varying gray values, separated by smooth boundaries, has been noted repeatedly. This failure can be discerned visually, in the form of characteristic compression artifacts, but it can also be derived theoretically. In this chapter, we review some of the constructions that were proposed as a remedy to this problem.We focus on twoconstructions: wedgelets [16] and curvelets [6]. Both systems stand for larger classes of image representation schemes; let us just mention ridgelets [4], contourlets [12,14], beamlets [17], platelets [35], and surflets [7] as close relatives.
