双层优化估计图像去噪问题的退火参数

Bilevel optimization approach for annealing parameter estimation in the image denoising problem

正则化参数的合理选取和有效利用是变分图像去噪问题中一个重要的问题。模拟退火算法利用迭代法逐步逼近能量泛函的最小解,并在迭代过程中单调地增加正则化参数。在一般情况下,模拟退火模型中的正则化参数/退火参数的确定和单调增加模式是基于经验的。希望通过数据自适应地学习最优的退火参数,文中将双层优化结构与模拟退火算法相结合,提出了一种新的估计退火参数的双层模型。下层是含有退火参数的迭代法,增加了Laplace附加正则项,以保证下层问题的良好性质;上层是基于L2范数度量的损失函数。同时,利用反向传播算法,提出了一种有效的估计退火参数的求解算法。并给出了一种简单的插值泛化方法,使提出的模型可以适应不同强度的噪声去除问题。实验结果表明,文中所提算法从数据中自适应学习的退火参数,满足模拟退火算法的先验性单增假定;对比常用正则化参数选取方法,所提算法在保证计算效率的同时提升了去噪效果;同时验证了所提算法具有很好的泛化能力。文中从数据学习的角度表明了迭代过程中正则化参数单调增加的合理性。进一步,说明了所提算法能够得到数值最优的退火参数和变化模式。

One of the important issues in variational image denoising is to select reasonable regularization parameters and use regularization parameters efficiently.The simulated annealing algorithm uses the iterative method to gradually approximate the minimum solution to the energy generalization function.The monotonically increasing regularization parameters are set in its iterative process.In general, the determination of the regularization parameters/annealing parameters and the monotonic increase pattern in the simulated annealing model are empirically based.In this paper, it is desired to learn the optimal annealing parameters adaptively from the data.The new bilevel model for estimating annealing parameters is proposed by combining the bilevel optimization structure with the simulated annealing algorithm.The lower level of the model is the iterative method containing annealing parameters, where the Laplace regularization term is added to ensure good properties of the lower level problem.The upper level problem is the loss function based on the L2norm.Meanwhile, this paper proposes an accurate solution algorithm for estimating the annealing parameters by utilizing the back propagation algorithm.A simple interpolation generalization method is given for adapting the proposed model to noise removal problems of different intensities.Experimental results show that the annealing parameters learned adaptively from the data by the algorithm proposed satisfy the assumption of increasing a priori monotonicity of the simulated annealing algorithm.Compared with common regularization parameter selection methods, the proposed algorithm not only ensures the computational efficiency but also improves the denoising effect.Experimental results also verify that the proposed algorithm has a good generalization ability.As shown in the paper, the reasonableness of the monotonic increase of the regularization parameters during the iterative process is demonstrated from the perspective of data learning.Further, it is shown that the proposed algorithm can be used to obtain numerically optimal annealing parameters and variation trends.