融合小波变换的分数阶全变分去模糊算法

Fractional-Order Total Variation Regularization Deblurring Algorithm Based on Wavelet Transform

摘要: 非盲图像去模糊是在已知模糊核的情况下，从给定的模糊图像中获得清晰的图像。在各种图像去模糊模型中基于全变分正则化的方法是有效的，然而，基于传统的全变分正则化方法存在阶梯效应，导致复原图像的边缘细节不够清晰，影响了恢复效果。针对泊松噪声下医学图像的复原问题，本文利用小波变换后高频图像具有稀疏性的特征，设计了一种将小波变换与分数阶全变分正则化模型相结合的图像复原算法。本文使用了交替方向乘子法对模型进行求解，将本文复原算法与RLTV、FOTV和BM3D三种算法进行实验对比。实验结果表明，在峰值信噪比和结构相似性的指标上，本文算法均优于以上几种算法。

Abstract: Obtaining a clear image from a given blurred image is the non-blind image deblurring when the blur kernel is known. The methods based on total variation regularization are effective in various image deblurring models. However, the traditional total variation regularization methods have the staircase effect, which makes the edge details of the restored images not clear enough and affects the restoration effect. Making use of the advantage of the sparsity of high-frequency images after wavelet transform, this paper designs an image restoration algorithm combining wavelet transform and fractional-order total variation regularization model, aiming at restoring medical images with Poisson noise. We used the Alternating Direction Method of Multipliers to solve our model. The proposed algorithm is compared with RLTV, FOTV and BM3D algorithms. Experimental results show that the proposed algorithm is superior to the above algorithms in terms of peak signal-to-noise ratio and structural similarity index.