Curvelets　are　used　to　deal　with　the　inverse　problem　of　recovering　a　function　f　from　noisy　Bessel　data　B　α　f　by　Candes　and　Donoho.　Motivated　by　the　work　of　Colona,　Easley　and　Labate,　we　solve　the　same　problem　by　shearlets.　It　turns　out　that　our　method　attains　the　mean　square　error　convergence　to　O(log(Ε-1)Ε2/3/2+α,　as　the　noisy　level　Ε　goes　to　zero.　Although　this　converge　rate　is　the　same　as　Candes　and　Donoho＇s　in　the　case　α　=　1/2,　the　shearlets　possess　affine　systems　and　avoid　more　complicated　structure　of　the　curvelet　constructure.　This　makes　it　a　better　candidate　for　theoretical　and　numerical　applications.　©　2011　Springer-Verlag　Berlin　Heidelberg.