Research On L₀ Edge-Preserving Filtering Based On Sparse Constraint

Edge-preserving filtering,where important edge features in an image are still maintained after filtering,has significant applications in the fields of computational photography and graphics.According to the difference of computational methods,traditional edge-preserving filtering algorithms are divided into local and global filtering.Local filtering methods use a weighted average of neighboring pixels to calculate the filtering result,which usually has high computational efficiency but tends to introduce halo artifacts.Global methods model the filtering as an optimization problem,which has stronger edge-preserving filtering capability,but has lower computational efficiency and is prone to introducing artifacts such as intensity shifts.Thus,how to improve the effectiveness and efficiency of image edge-preserving filtering is an urgent problem to be solved.With the sparsity of its solutions,L0-norm smoothing filtering has achieved remarkable results in edge-preserving filtering.However,the method still has some shortcomings,such as the filtering results are prone to intensity shift artifacts,and the low computational efficiency is not suitable for real-time applications.To address the shortcomings in the traditional algorithm,this thesis proposes a new global edge-preserving filtering method for solving L0 gradient regularized problem,i.e.,the L0 image edge-preserving filtering method based on truncated L1-norm gradient regularization.The specific work is as follows:(1)To improve the edge-preserving capability and filtering effect of the filtering method,this thesis uses an iterative strategy where each iteration is an optimization problem based on truncated L1 gradient regularization,which can be efficiently solved using alternating direction multiplier method and Fourier domain optimization algorithm.The gradient shift during the iteration is restricted by using the L1-norm,thus alleviating various artifacts of the conventional L0 filter.Through comparative experiments,it was verified that the method proposed is applicable to a variety of image applications.(2)To improve the computational efficiency of the proposed method,a convolutional neural network is introduced and an unsupervised learning based adjustable parameter L0 filtering method is proposed.Adjustable parameters,i.e.,for the same image,if the input parameters are different,the filtering results are different.The method uses the above iterative L1-norm as the loss function,and to achieve adjustable parameters,the input data contains images,truncated gradients,and changing filtering parameters.Through experimental comparison,the method not only has superior filtering effect,but also has a greater advantage in computational efficiency.(3)Based on the above research,a sparse constraint-based L0 edge-preserving filtering image processing system is designed and implemented.The system integrates five computational photography applications,the core of each application being based on the two methods proposed in this thesis.In addition,the system provides a very user-friendly interactive experience,with different effects depending on the user’s choice.The implementation of this prototype system demonstrates that this research is not only highly relevant at a theoretical level,but also has practical value in the engineering field.