Abstract: CT reconstruction from insufficient data is important in many medical and other applications.Recently to solve this under-determined problem,the Total Variation minimization method has regained popularity due to the newly-emerging compressed sensing theory.In this paper TV-minimization is extended to a more general framework for CT reconstuction from insufficient data.The framework proposed is also based on the compressed sensing theory,but is more flexible and amenable to various applications.Analysis and simulations are conducted for an initial special case and promising results are achieved.