The goal of digital image restoration is to reconstruct an original scene from a degraded observation. This recovery process is critical to many image processing applications. The digital image restoration approaches has been thoroughly studied in recent years. This problem

however

still has numerous research possibilities. In order to give people a comprehensive knowledge of digital image restoration

some typical approaches are presented and discussed in this paper based on 95 references selected from various literatures in this field. We first describe problems in the digital image restoration and discuss its mathematics background. And then

the review is divided into two parts and discussed thoroughly

according to the development of digital image restoration approaches. One is the classical image restoration approaches

and the other is the modern ones. The former is developed based on the objective that provides an overview on the basic principles and methodologies behind the existing algorithms

and the later is arranged to examine the current trends and the potential of this challenging problem. After the survey is discussed in detail

we make a conclusion for this paper and follow by addressing 7 key issues which remain open in this field.