Abstract:

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 L₂ norm.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.

Key words: image denoising, simulated annealing, bilevel optimization, annealing parameters