06045874

j

06045874 Grohs, P. Tree approximation with anisotropic decompositions. Appl. Comput. Harmon. Anal. 33, No. 1, 44-57 (2012). 2012 Elsevier Science (Academic Press), Orlando, FL EN shearlets curvelets tree approximation bit rate coding

doi:10.1016/j.acha.2011.09.004

It is known that for the $L_p({\Bbb R})$-approximation of Besov balls in a wavelet basis the additional assumptions on the set of coefficients to possess a tree structure does not deteriorate the $N$-term approximation rate. In this paper analogous results for the $L_2({\Bbb R}^2)$-approximation of cartoon images with smooth discontinuity curves by anisotropic transforms based on parabolic scaling, e.g. shearlets or curvelets, are proved. As an application the (almost) optimal encoding schemes for cartoon images are constructed. Yuri A. Farkov (Moscow)