Theoretical Analysis And Algorithm Of ROF Model For Image Denoising

Image is one of the important sources of information for people.Limited by imaging,transmission,storage and other technologies,images are often polluted by noise.Therefore,how to remove the noise in images,namely image denoising,has always been a challenging and realistic work in the field of image processing.The traditional image denoising methods are based on the linear system to use the inverse filtering to restore the original image,but they will smooth the edge in images.Especially,there may be "ringing" phenomenon when the noise is strong.Rudin,Osher and Fatemi proposed a classical Total Variation(TV)denoising model,namely,the famous ROF model.The model has stronger ability to protect the image edge.However,the authors don't prove the existence and uniqueness of the solution of the model.In addition,they employ explicit finite difference scheme to numerically solve the gradient descent flow equation corresponding to the model.Because of the limitation of Courant-Friedrichs-Lewy(CFL)condition,the time step must take small to ensure the stability of numerical calculation,which results in the greater number of iterations and time-consuming computation.To addressing the above problems,this thesis focuses on the theoretical analysis and the numerical algorithm of the ROF model.In the numerical algorithm,this thesis proposes a semi-implicit finite difference scheme to numerically solve the gradient descent flow equation of the ROF model,which allows larger time step.In the theoretical study,this thesis gives a novel proof of the existence and uniqueness of solution of the ROF model,and proves the stability and convergence of the proposed numerical algorithm.Experimental results on noisy images with Gaussian or Poisson noise show that the proposed algorithm has better effect on denoising and faster convergence speed than the original algorithm and some other related algorithms.