基于自适应加权低秩矩阵恢复的图像去噪

Image denoising based on adaptive weighted low-rank matrix recovery

针对基于低秩矩阵恢复的图像去噪算法存在难以分离低秩信息与噪声,以及存在经验超参数而导致性能差的问题,提出一种基于自适应加权低秩矩阵恢复的去噪算法.首先利用图像非局部相似先验构建低秩去噪模型,然后引入Gerschgorin理论从观测矩阵中准确估计出低秩矩阵的秩.在此基础上,结合秩估计方法提出自适应加权思想,通过奇异值分解(SVD)与加权软阈值算子对自适应加权低秩去噪模型进行求解,得到最终的去噪图像.实验结果表明:本算法与现有的多种经典去噪算法相比,获得了更高的平均峰值信噪比(PSNR)和结构相似性(SSIM)指标,对含有较高强度(方差为100)噪声的图像去噪平均PSNR和SSIM指标分别达到24.66 dB和0.7267,对含有真实噪声的图像去噪也取得了更好的效果.

Aiming at the issues of poor performance due to the difficulty of separating low-rank information from noise and existing empirical hyperparameters in the image denoising algorithm based on low-rank matrix recovery,a denoising algorithm based on adaptive weighted low-rank matrix recovery was proposed.First,a low-rank denoising model was constructed using the image nonlocal similarity prior,and then the Gerschgorin theory was introduced to accurately estimate the rank of the low-rank matrix from the observation matrix.On this basis,an adaptive weighting ideology was presented in combination with the rank estimation method,and the adaptive weighted low-rank denoising model was solved by singular value decomposition(SVD)with the weighted soft threshold operator to obtain the final denoised image.Experimental results show that the proposed algorithm could obtain higher average peak signal-to-noise ratio(PSNR)and structural similarity(SSIM)compared with several existing classical denoising algorithms,which could achieve average PSNR of 24.66 dB and SSIM of 0.7267 for denoising images with high intensity noise(the variance is 100),and could also achieve better results for denoising images with real noise.