基于改进的MCA和K-SVD的图像稀疏表示去噪算法

Image denoising via the sparse representation based on improved MCA and K-SVD

图像去噪是图像处理中的关键问题之一,传统的图像去噪方法是基于小波阈值变换的,其去噪效果较好,但容易丢失细节信息,导致边缘模糊,针对传统去噪方法存在的不足,本文提出一种基于形态学成分分析(Morphological Component Analysis,MCA)和K奇异值分析(K-SVD)的图像去噪方法.考虑到传统的MCA算法对图像的稀疏性要求较高,本文通过求解最接近l1范数的若干次优解和最小l1范数解进行加权叠加,并将结果作为源信号的估计,改进了传统MCA算法中对图像稀疏性的高要求,提高了对源信号估计的精度.本文方法首先采用改进的MCA算法将含噪图像划分为平滑部分、纹理部分和边缘部分;然后对平滑的结构部分采用小波阈值去噪,并利用改进的K-SVD去噪算法对纹理部分和边缘部分进行自适应去噪,最后将三部分合起来得到最终去噪图像.实验表明,该方法相比于传统的图像去噪方法能够更好地滤除噪声,保留图像的细节特征和边缘信息,获得更高的峰值信噪比值.

Noise removal plays an important role in image processing. Traditional image denoising meth- od is wavelet denoising and get better performance but can loss details and lead to edge blurring. An im- age denoising method based on （Morphogonal Component Analysis） MCA and K-SVD algorithm is carried out in this paper to overcome above drawbacks. Considering the demand of the image sparsity is higher via traditional MCA. This paper endeavors to search the optimal minimum solution of ll-norm and the suboptimal solutions which are close to the minimum ll-norm, and then weighted sum of these two parts is taken as the estimation of the sources. This method improves the performance of high demand to image sparsity. In this paper, first the outhors decompose the image into structure image, tex- ture image and edge image by improved MCA . Second denoise the structure part via wavelet technique and the other two parts are processed by improved K-SVD. Simulation results show that our method can get better denoising performance both in PSNR value and visual effects.