组稀疏表示的双重l1范数优化图像去噪算法

Double l1-norm optimization image denoising algorithm via group sparse representation

摘要:

由于图像受噪声的影响，无法从降质信号中获得准确的稀疏系数.针对此问题，对一种组稀疏表示的双重l1范数优化图像去噪算法进行研究，该算法同时采用非局部相似图像块组稀疏表示的l1范数和稀疏残差作为正则项对组稀疏系数进行约束，并利用一种有效的迭代收缩算法实现对模型的优化求解，以获取了更鲁棒的稀疏系数，另外，为了进一步提高去噪性能，采用贝叶斯公式推导出自适应调整两个正则化参数的方法.实验结果表明，与现有的许多算法相比，新算法能够在去除噪声的同时抑制伪影，保护图像的细节信息，峰值信噪比相对经典的BM3D算法而言，最多可提高1.24dB.

Abstract:

The accurate sparse coefficients were hard to be obtained from the degraded signal due to theimage noise. Aiming at this problem, a double l1norm optimized image denoising algorithm via group sparse representation is studied. The algorithm constrains group sparse coefficients by using the l1norm and sparse residual of sparse representation of nonlocal similar image block as regularization item, and implements an optimal solution to the model for obtaining robust sparse coefficients by an effective iterative shrinkage algorithm. In addition, in order to further improve the performance of the image denoising algorithm, a Bayesian formula is used to derive a method for adaptively adjusting two regularization parameters. Extensive experimental results show that the proposed algorithm can suppress the artifacts while removing image noise, and preserve the detail of the image compared to many existing algorithms. Compared with the BM3D algorithm, our algorithm significantly improves the performance by 1.24 dB in PSNR.