Multiplicative Noise Removal And Blind Inpainting Of Ultrasound Images Based On A New Variational Framework

Multiplicative noise removal and image inpainting are two important preprocessing steps and are widely used in image and visual analysis.In some applications,multiplicative noise and intensity missing always exist at the same time.So,the purpose of this paper is to propose a new and more efficient model to remove the multiplicative noise,meanwhile estimate the location of missing pixels and fill in them.Firstly,a new mathematical description is given for degraded images with multiplicative noise and partial signal missing.Based on the new degradation model and the maximum a posterior(MAP)estimation,a new variational framework is proposed when the locations of the damaged pixels are unknown.Under this framework,we propose three models for simultaneous multiplicative noise removal and blind inpaintng.In order to suppress the noise and fill in the missing intensities,we apply space regularization:total variation(TV),total generalized variation(TGV)and fractional-order total variation(FOTV),to the ideal images for smoothing outliers andl₀ norm to the artifacts for sparsely regularization.By taking into account the statistical distribution of multiplicative noise as Gamma or Rayleigh noise,we give the special data fidelity term.So three models,TV-l₀,TGV-l₀ andFOTV-l₀,are presented for Gamma and Rayleigh noise.Due to the non-convexity and non-differentiability of the proposed minimization problem,we introduce additional auxiliary variables and then use the alternating direction method of multipliers(ADMM)to solve the proposed models.Finally,the compared model and the proposed models are used to reconstruct the synthetic degraded images and real medical ultrasound images.The experimental results show that the proposed models can efficiently remove the multiplicative noise and fill in the missing pixels.Compared to the TV regularization,the TGV and FOTV regularization can not only preserve the edges and texture details of an image,but also avoid the staircase effect.In addition,the numerical results also show that among these models the FOTV regularization is most effective in image restoration.