同伦方法在图像稀疏去噪中的应用

本文在深入研究稀疏表示和字典学习理论的基础上，建立了图像去噪模型并提出一种新的图像去噪算法。该算法采用同伦方法学习字典，充分利用了同伦方法收敛速度快以及对信号的恢复准确度高的特点。之后利用 OMP 算法求出带噪图像在该字典下的稀疏表示系数，并结合稀疏去噪模型实现对图像的去噪。实验结果显示本文算法在不同的噪声环境下具有较好的去噪效果，同时在与 K-SVD 算法关于收敛速度比较的实验中，实验结果充分显示了使用同伦算法学习字典在收敛速度上的优势。 

Homotopy Method for Sparse Model and Application to Image Denoising

In this paper, we establish an image denoising model and propose a new image denoising algorithm based on the study of sparse representation and dictionary learning theory. Homotopy method is used to learn a dictionary, which has the characteristics of fast convergence speed and high accuracy in signal recovery. As we can use the OMP algorithm to derive the sparse representation of the noisy image with respect to the learned dictionary, which is learned by the homotopy method, then by combining the sparse denoising model we can use our proposed method to denoise the noisy image. Experiment results show that the proposed algorithm can achieve nice performance for different noise environments. In the experiment of comparing the convergence speed with K-SVD algorithm, the experiment results sufficiently show that the proposed method has faster implementation than K-SVD which fully displays the advantage of using the homotopy method in learning a dictionary.