基于小波阈值和全变分模型的图像去噪

针对小波阈值函数去噪不彻底并且造成图像边缘模糊的问题，提出一种自适应小波阈值和全变分模型相结合的去噪方法。利用小波变换的时频域特性将含噪图像分解得到各维度小波系数，对低频小波系数利用全变分模型去噪，对于高频系数根据不同分解尺度选择不同的最佳阈值去噪，克服了统一阈值的不足，增强了算法的自适应性。理论分析和仿真实验结果表明，所提方法兼顾了小波变换和全变分模型的去噪优点，在有效去除噪声的同时更完整地保留了图像的边缘和细节信息，有较高的结构相似度和峰值信噪比。

Method for image denoising based on wavelet transform and total variational model

As the drawbacks of traditional wavelet threshold algorithm for image noise reduction that it can not eliminate the noise thoroughly and blur the image edge, this paper proposed an image denoising method based on wavelet transform and total variation model. Firstly, the wavelet coefficients of each dimension separated from the noisy image through the wavelet transform, then used the total variation model to filter the low frequency coefficients, and for the high frequency coefficients, different thresholds in different decomposition scaled for eliminating the noise overcame the lack of the universal threshold and enhanced the adaptability of the algorithm. Finally, the wavelet inversion obtained the denoised image. Theoretical analysis and experimental results show that this algorithm with the advantages of both wavelet transform and total variation model, it can remove noise effectively, keep image edges and details very well, the structural similarity and peak signal-to-noise ratio have also improved.