On Convergent Finite Difference Schemes for Variational - PDE Based Image Processing
This is an incremental improvement in image processing for denoising applications, offering better convergence rates for edge-preserving restoration.
The paper tackles image denoising by developing an adaptive anisotropic Huber functional model that combines L2-L1 regularization for edge preservation, and presents a convergent finite difference scheme using Split Bregman to find the discrete minimizer. The result shows that their algorithm achieves the best convergence rates compared to additive operator splitting, dual fixed point, and projected gradient schemes.
We study an adaptive anisotropic Huber functional based image restoration scheme. By using a combination of L2-L1 regularization functions, an adaptive Huber functional based energy minimization model provides denoising with edge preservation in noisy digital images. We study a convergent finite difference scheme based on continuous piecewise linear functions and use a variable splitting scheme, namely the Split Bregman, to obtain the discrete minimizer. Experimental results are given in image denoising and comparison with additive operator splitting, dual fixed point, and projected gradient schemes illustrate that the best convergence rates are obtained for our algorithm.