Data denoising is a classic issue in the field of signal and image processing which has been widely applied in various engineering practices. Due to the diversity of noise sources, denoising is a challenging and active research topic, and a variety of classical denoising methods have been developed. In recent years, with the development of compressed sensing theory, the methods for solving inverse problem based on sparse representation and regularization constraint have become important research directions and technical approaches in the field of image denoising. This paper firstly reviews and summarizes the sources and types of image noise, and then according to the different types of image noise, gives a comprehensive review focusing on the image denoising techniques based on sparse representation and regularization constraints. In addition, we analyze and describe the principle, advantages and disadvantages of several major denoising methods. Finally, the performance evaluation of denoising algorithm is summarized.