Traditional redundant dictionary can not represent the image features self-adaptively.In order to overcome this drawback,this paper presents an optimal image dictionary construction algorithm.The algorithm establishes a novel optimal pri nciple,using grey relational theory to analyze the value in a redundant dictionary.First we choos e grey relation to express the relation between atoms and their characters in dictionary.The value of grey relation of atoms can present their characteristics and measure their relations,and it ca n be the criteria to realign the atoms in dictionary.Then we optimize the arrays of atoms according to the value of grey relation and it can express different characteristics in different areas of an image.Finally,we construct an adaptive dictionary which accords with the local and whole characte ristics in image by the model of grey relational value and noise.The new method provides an efficient w ay to measure the relation between atoms in image dictionary and a better way to express image structure characteristics.It can select redundant factors of dictionary adaptively accordi ng to the image structure and noise information.The experimental results show that the proposed algorithm enhances the dictionary recovery ability significantly and improves the efficien cy and the denoising effect greatly.