A bilateral optimization iteration CT reconstruction method for incomplete projections

•A new incomplete projection reconstruction algorithm was proposed based on the discussion of key points in iteration, rather than some specific reconstruction method.•The iteration process was improved from the two aspects of initial value and restraint equations.•The reconstructed quality of new method was better than conventional methods for both model image and actual experimental image.•The particle in local region was reconstructed better while it was wrongly recognized as two small particles using conventional methods.