中文摘要：

磁共振图像的降噪处理一直是医学图像处理中重要的研究领域。图像中存在噪声会降低图像质量从而影响临床诊断。现有K-SVD算法虽然能达到良好的去噪效果。但却在字典训练中消耗大量时间。本文针对时间消耗问题，提出利用改进的K-SVD算法进行医学图像去噪。首先根据已知的字典原子的可稀疏性，提出一种高效、灵活的稀疏字典结构，该字典能够提供高效的前向和伴随算子。并具有紧凑的表示形式，同时可以有效地训练图像信号；然后在现有K-SVD算法的基本框架下，结合字典的稀疏表示特点使用改进K-SVD算法训练稀疏字典，改进的K-SVD算法能够对更大的字典进行训练，特别是对高维数据的处理更具有优势。实验结果表明，该算法相对基于离散余弦变换字典的磁共振图像去噪以及基于传统K-SVD算法的磁共振图像去噪，不仅能够更加有效地滤除图像中的高斯白噪声，更好地保留原图像的细节信息，而且有效降低了字典训练所消耗的时间；在相同的噪声标准差下，改进K-SVD算法的峰值信噪比提高了约1～3dB。

英文摘要：

Magnetic resonance image is an important research field in medical image processing. Because it can degrade the image quality, the signal noises have a negative impact on clinical diagnosis. The K-SVD algorithm can obtain better de-noising results, but the time-consuming problem of the dictionary training still exists. A medical image denoising algorithm based on improved K-SVD is studied to solve this problem. First of all, an efficient and flexible dictionary structure is proposed based on a sparsity model of the dictionary atoms over a know dictionary. The sparse dictionary provides efficient forward and adjoint operators, has a compact representation, and can be effectively trained from given example data. Then the basic framework of the existing K-SVD algorithm, combined with the dictionary sparse representation, can improve K-SVD training algorithm, and the improved K-SVD algorithm can be trained for greater dictionary, especially for high-dimensional data. Therefore, it can be used to remove the noise of magnetic resonance images. The experimental results show that the algorithm, in comparison with the discrete cosine transform dictionary and conventional K-SVD algorithm, can effectively filter Gaussian white noise of the image to retain image details, and reduce the time of dictionary training. It is found that the peak signal-to-noise ratio is increased by about 1-3db with the prooosed method.