A fractional variational image denoising model with two-component regularization terms

•A two-component variational image denoising model is established.•The existence and uniqueness of solution for the variational model are proved.•A numerical algorithm for this model is proposed to validate the theoretical resultsl.•The efficiency of our numerical method is tested by comparing with some other published works. Image denoising is to recover true image from noisy image. Many image deonising models are proposed during the last decades. Some models preserve the margin of tissue, i.e., TV model, while the others, i.e., LLT model, prefer smooth solutions. By decomposing true image into cartoon part and texture part, we propose a fractional image denoising model with two-component regularization terms. Setting some appropriate parameters, the proposed model can deal with both smooth and non-smooth image denosing problems. The existence and uniqueness of solution for the variational model are proved. Moreover, a Split-Bregman(S-B) based numerical algorithm to solve this model is also proposed to validate the theoretical results. Numerical tests show that the proposed model can produce competitive denoising result to the other three published models.