Local and international survey research on the convex energy functional regularization model(EFRM) are rare. To obtain comprehensive understanding of potential research

research development is surveyed in the field. Based on numerous references

we summarize and compare convex EFRM from four aspects

namely

original

composition

treatment

and development. First

given the inverse problem

obtaining feasible solutions is impossible. The effective method of solving the problem is to establish EFRM. Second

after establishing the energy functional model

the application conditions of the fitting and regularization terms are analyzed. Five types of point spread functions that can make image blur are provided. The significance and weight determination method are presented. Third

the fitting and regularization terms of the energy functional model are sorted by entire and separate treatments

and the computational algorithms of the regularization model are analyzed in space

transform

and hybrid domains. The advantages and disadvantages of the models and algorithms are determined. Finally

the development trends and existence problems of EFRM of image restoration are highlighted. Generally

directly solving primal convex EFRM is impossible; however

with transformation model

dual model

and primal-dual model of the primal model and by taking advantage of numerical analysis

matrix theory

and optimization theory

designing effective and rapid algorithms to completely and separately solve the transformation model becomes possible. Meaningful theories and applicable results of EFRM of image restoration have been obtained. However

with the continuing appearance of large-scale data processing problems

several theoretical problems

such as establishment of accurate mathematical models

design of effective and fast solving algorithms

and analysis of algorithm convergence properties

require further research.