Study Of Image Restoration Algorithm Based On Cosparse Model

In recent years, the image restoration algorithm based on sparse representation model has been widely concerned. Sparse representation of images includes two model s, namely synthesis model and analysis model. Under the condition of the same dimension, the number of the subspace in the analysis model is more than the synthesis model. What’s more, the analysis model has a richer and more flexible expressing ablility comparing with the synthesis model. This paper focuses on the application of the image sparse representation based on the analysis model on the image restoration issue.The main work are as follows:Firstly, this paper puts forward a new algorithm of restoration based on the Cosparse analysis model in the framework of the sparse representation. This paper uses the Coparse analysis dictionary, which is obtained by the geometric conjugate gradient learning algorithm, leading to a sparse representation of image. In the algorithm, the problem of image restoration is expressed as the sparse regularization problem. At the same time, by introducing the alternating direction method of multipliers to optimize the issue, the restored image is obtained. The experimental results show that the images blurred by different type of blur are well restored.Secondly, aiming to make full use of prior knowledge of the image, this paper proposed a new image restoration algorithm introducing both the Cosparse analysis model leading to a sparse representation of each image patch and translation invariant wavelet transform leading to a sparse representation over the whole image. In the algorithm, the problem of image restoration is expressed as the double sparse regularization problem, and then the restored image is obtained by using the alternating direction method of multipliers. Experiments show that the proposed algorithm can effectively improve the quality of restored images.Finally, this paper realized the estimate of the blur kernel combining the spectrum of the blur kernel, which is obtained by using the spectrum estimation method. And then the restored image is obtained using a non-blind image restoration algorithm. Experiments verified the effectiveness of the proposed algorithm.