The　Radon　transform　plays　an　important　role　in　applied　mathematics.　It　is　a　fundamental　problem　to　reconstruct　images　from　noisy　observations　of　Radon　data.　Compared　with　traditional　methods,　Colona,　Easley　and　etc.　apply　shearlets　to　deal　with　the　inverse　problem　of　the　Radon　transform　and　receive　more　effective　reconstruction.　This　paper　extends　their　work　to　a　class　of　linear　operators,　which　contains　Radon,　Bessel　and　Riesz　fractional　integration　transforms　as　special　examples.