A new local and nonlocal total variation regularization model for image denoising

The total variation (TV) method for image deblurring is effective for sharpening image details in noisy images although this method tends to over-smooth the image details and inevitably results in staircase effects in smooth areas of the image. The nonlocal total variation (NLTV) method overcomes these drawbacks and retains fine details. However, it is not suitable for detecting similar patches and usually blurs edges in the image. Considering that the TV and NLTV are complementary, we propose a new local and nonlocal total variation (LNLTV) model. In this model, we first decompose the original image into a cartoon component and a detail component, then respectively apply the TV and NLTV to both components. To optimize the hybrid model, the Bregman iteration-based multivariable minimization (BIMM) method and the fast iteration-based multivariable minimization (FIMM) method are respectively employed to minimize the LNLTV energy function. The experimental results clearly demonstrate that the LNLTV model has better performance than some other state-of-the-art models with regard to evaluation indices and visual quality, and the FIMM method has a faster convergence rate and requires less time than the BIMM method.