基于K-SVD的偏微分方程模型在毫米波图像恢复中的应用

摘要

When an image contaminated by large noise or with lower resolution is processed by the traditional Partial Differential Equation (PDE) model, the stable solutions of PDE can generate a distinct step effect and the restored image's quality is relatively poor. Therefore, a new PDE image restoration method based on K-Singular Value Decomposition (K-SVD) was proposed and used successfully to restore MilliMeter Wave (MMW) image. K-SVD was a sparse representation method of images. An image can be denoised when it is sparsely estimated by K-SVD. Especially, for images with large noise variance, K-SVD has better denoising robustness. At first, the MMW image was denoised by /C-SVD, and then PDE method based on Total Variation (TV) was utilized to restore the denoised images obtained by K-SVD. In test, a simulated MMW image and a real MMW image were used respectively to testify the proposed algorithm, and then the results were compared with those of K-"SVD and PDE. At the same time, the Pick Signal-to-Noise Ratio (PSNR) criterion was used to measure restored images. In terms of PSNR values and the vision effect of restored images with different noise variance, the simulation results show that the proposed method can efficiently denoise MMW images.%在图像被大噪声污染或具有较低分辨率时,传统的偏微分方程(PDE)模型的稳态解会产生明显的阶梯效应,恢复图像质量较差.针对此缺点,提出了一种新的基于K-奇异值分解(K-SVD)的PDE图像恢复方法,并应用于毫米波(M MW)图像的恢复.K-SVD是一种图像稀疏表示方法,对图像进行稀疏估计的同时实现去噪,对噪声方差较大的图像具有较好的去噪鲁棒性.首先采用K-SVD对MMW图像进行去噪,对去噪图像再应用全变分(TV)模型的PDE方法进行恢复.对所提出的算法分别使用模拟的MMW图像和真实的MMW图像进行测试,并进一步和K-SVD、PDE方法比较,同时使用峰值信噪比(PSNR)对恢复图像进行评价.根据不同噪声方差下的PSNR数据和恢复图像的视觉效果,实验结果证明了所提方法能够有效地恢复MMW图像.