Abstract:

Aiming at the denoising problem in image restoration, an adaptive weighted encoding and L_1/2 regularization method was proposed. Firstly, for many real images which have not only Gaussian noise, but have Laplace noise, an Improved L₁-L₂ Hybrid Error Model (IHEM) method was proposed, which could have the advantages of both L₁ norm and L₂ norm. Secondly, considering noise distribution change in the iteration process, an adaptive membership degree method was proposed, which could reduce iteration number and computational cost. An adaptive weighted encoding method was applied, which had a perfect effect on solving the noise heavy tail distribution problem. In addition, L_1/2 regularization method was proposed, which could get much sparse solution. The experimental results demonstrate that the proposed algorithm can lead to Peak Signal-to-Noise Ratio (PSNR) about 3.5 dB improvement and Structural SIMilarity (SSIM) about 0.02 improvement in average over the IHEM method, and it gets an ideal result to deal with the different noise.

Key words: L₁-L₂ Hybrid Error Model (HEM), adaptive membership degree, weighted encoding, sparse solution, L_1/2 regularization

摘要：

针对图像重建过程中噪声去除问题,提出一种自适应加权编码L_1/2正则化重建算法。首先,考虑到许多真实图像中不仅含有高斯噪声,而且含有拉普拉斯噪声,设计一种改进的L₁-L₂混合误差模型(IHEM)算法,该算法兼顾了L₁范数与L₂范数的各自优点;其次,由于迭代过程中噪声分布会发生改变,设计一种自适应隶属度算法,该算法可以减少迭代次数和运算时间;利用一种自适应加权编码方法,该方法可以有效地去除含有重尾分布特性的拉普拉斯噪声;另外,设计一种L_1/2正则化算法,该算法可以得到较稀疏的解。实验结果表明,相比IHEM算法,自适应L_1/2正则化图像重建算法的峰值信噪比(PSNR)平均提高了3.46 dB,结构相似度(SSIM)平均提高了0.02,对含有多种噪声的图像处理具有比较理想的效果。

关键词: L₁-L₂混合误差模型, 自适应隶属度, 加权编码, 稀疏解, L_1/2正则化