对偶算法在紧框架域TV-L1去模糊模型中的应用

目的 建立准确的数学模型并获得有效的求解算法是图像恢复面临的“两难”问题,非光滑型能量泛函有利于准确描述图像的特征,但很难获得有效的求解算法。提出一种拟合项和正则项都是非光滑型能量泛函正则化模型,并推导出有效的交替迭代算法。方法 首先,对系统和椒盐噪声模糊的图像,在紧框架域,用L₁范数描述拟合项,用加权有界变差函数半范数描述正则项。其次,通过引入辅助变量,将图像恢复正则化模型转化为增广拉格朗日模型。再次,利用变量分裂技术,将转化模型分解为两个子问题。最后,利用Fenchel变换和不动点迭代原理,将子问题分别转化为对偶迭代子问题和松弛迭代子问题,并证明迭代子问题的收敛性。结果 针对图像恢复模型的非光滑性,提出一种交替迭代算法。仿真实验表明,相对传统算法,本文算法能有效地恢复系统和椒盐噪声模糊的图像,提高峰值信噪比大约0.51分贝。结论 该正则化模型能有效地恢复图像的边缘,取得较高的峰值信噪比和结构相似测度,具有较快的收敛速度,适用于恢复椒盐噪声模糊的图像。

Application of dual algorithm to TV-L1 deblurring model of frame domain

Objective Establishing an accurate mathematical model and a design-effective algorithm is a dilemma in image restoration. The non-smooth energy functional model effectively describes image features but is difficult to use in a design-efficient computational algorithm. In this study, a new non-smooth energy functional regularization model that consists of fitting and regularization terms is developed. An efficient alternative iterative algorithm is deduced. Method First, for an image made blurry by system and salt-and-pepper noise in a tight frame domain, the fitting term is described by the L₁ norm;the regularization term is established by the semi-norm of a weight-bound variation function. Second, the regularization model of image restoration is converted into an augmentation Lagrange model by introducing an auxiliary variable. Third, the transformed model is decomposed into two sub-problems by employing the variable splitting technique. Finally, by employing Fenchel transform and the fixed-point iterative principle, the sub-problem is transformed into dual and relaxed iterative sub-problems. The convergence property of the sub-problems is proven. Result An alternate iterative algorithm is proposed for the non-smooth property of the image restoration model. Compared with traditional algorithms, the proposed algorithm can effectively restore blurry images made so by system and salt-and-pepper noise and can increase the peak signal-to-noise ratio to approximately 0.5 dB to 1 dB. Conclusion Results show that the proposed algorithm can effectively protect image edges and can achieve a high peak signal-to-noise ratio and structural similarity index measure. The proposed algorithm also has high convergence speed and can restore images rendered blurry by salt-and -pepper noise.