一种改进K-SVD稀疏表示图像去噪算法

为解决传统K-奇异值分解(K-SVD)算法字典训练耗时过长以及低信噪比情形下去噪效果不佳的问题，提出了一种改进算法。首先将原始含噪图像进行高低频分离，然后对图像的高频部分使用基于残差比阈值的批量正交匹配追踪算法(Batch-OMP)实现稀疏重构，最后将图像的高低频部分叠加完成最终的去噪。实验结果表明，相较于小波变换去噪、DCT稀疏表示去噪以及传统K-SVD稀疏表示去噪，改进的算法能够更好地保留图像的边缘轮廓信息，并且去噪时间明显缩短。

An image denoising algorithm via sparse and redundant representations over improved K-SVD algorithm

To solve the problem that the traditional K-Singular Value Decomposition(K-SVD) algorithm dictionary training is too time-consuming and the de-noising effect is poor under low signal-to-noise ratio, an improved algorithm is proposed. Firstly, the original noisy image is separated by high and low frequencies; Secondly, on the basis of residual ratio threshold, the Batch-Orthogonal Matching Pursuit(Batch-OMP) algorithm is applied for the high frequency part of the image to realize the sparse reconstruction. Finally, the high and low frequency parts of the image is superimposed to complete the final denoising. The experiments show that the proposed algorithm can better preserve the edge contour information of the image, and the time of denoising is obviously shorter than that of wavelet transform denoising, DCT sparse denoising and traditional K-SVD sparse denoising.