Recently a number of algorithms have been proposed to overcome the data insufficiency for certain compressible signals.Most of the existing methods are appropriate for piecewise smooth objects

but do not behave very well on texture-rich object.In this paper

a new optimization model for tomography reconstruction for texture-rich object is proposed based on morphological components analysis

in which compound regularizations are exploited.Furthermore

an alternating iterative algorithm is presented to solve the relevant optimization problem.We compare its numerical performance with two recent algorithms

which demonstrate that the proposed method is highly efficient especially in preserving texture features.