To overcome the texture loss and false edge caused by a bounded variation function

a mixing regularization model in a tight frame domain that protects image texture information and reduces false edge is proposed. An alternating-direction iteration multiplier algorithm is introduced. First

in the tight frame domain

for images blurred by system and Poisson noises

the fitting term is described by the Kullback-Leibler function

the mixing regularization terms are composed of the semi-norm of the bound variation function and the L norm

and the fitting and weight regularization terms constitute the energy functional regularization model. Second

the solution and uniqueness of the mixing regularization model are analyzed. Third

the minimum problem of the mixing regularization model is decomposed into four easily solved sub-problems by introducing auxiliary variables and utilizing the alternating-direction iteration multiplier algorithm. Finally

an effective optimization algorithm is constructed with the four sub-problems via alterative iteration. The mixing regularization of the tight frame domain can effectively overcome the texture information loss and false edge caused by the bound variation function. Compared with traditional algorithms

the proposed algorithm can increase the peak signal-to-noise ratio to approximately 0.1 dB to 0.7 dB. The proposed model can protect image texture information

alleviate false edges

achieve higher peak signal-to-noise ratio and structural similarity index measure

and restore images blurred by system and Poisson noises compared with other regularization models.