It is an important and indispensable part for image compression to evaluate its results. Quality assessment methods for image compression can not only evaluate the quality of the results, but also, to a certain extent, judge the methods of image compression. This paper firstly introduces several common objective assessment methods for image compression and the progress of recent research. Then, aiming at the shortage of existing blind assessment methods, it provides a blind assessment method for image compression quality based on edge detail restoration and artifacts elimination. Experimental results show that it is an effective method.