Research On Image Restoration Algorithm Based On Bounded Constraint Total Variation

The regularization algorithm of total variation has been proved to apply to image restoration,and can retain some important texture information of the image,but this may produce some staircase effects for the reconstructed image.In addition,it is well-known that recovering by inverting is an ill-posed problem because the solution is highly sensitive to the noise,so the fast speed solution of total variation regularization algorithm has always been a frontier research topic.In this paper,based on total variation regularization,we discuss the fast algorithm of image restoration under different noises.For the image restoration of Gauss noise,based on the total variation image restoration model,a fast algorithm for the constrained total variation image restoration is proposed.In the proposed algorithm,the primal problem is transformed into three sub-problems,and the iterative threshold method,Fourier transform method and projection method are used to be solved the sub-problems respectively.In the solution of the fidelity term,the fast iterative technique is applied to the iterative threshold method to accelerate the efficiency of the algorithm.The inexact method can be used to overcome the slow computation speed of the Fourier transform for random projection matrix.Then,for image restoration with impulse noise,we propose a fast algorithm based on the bounded constrained total variation.The new algorithm transforms the original problem into four sub-problems with fast techniques and the alternating direction method of multipliers.Twice threshold methods,Fourier transform method and projection method are used be solve the sub-problems respectively.In the solution of the constrained term,the fast iterative technique is applied to the projection method to accelerate the efficiency of the algorithm.The above general variational regularization algorithm can also effectively restore the Poisson noise image.For image restoration with Poisson noise,we propose a fast algorithm based on the bounded constrained total variation.The new algorithm transforms the originalproblem into four sub-problems with fast techniques and the alternating direction method of multipliers.The shrink threshold method,Fourier transform method and projection method are used be solve the problems.In the solution of the constrained term,the fast iterative technique is applied to the projection method to accelerate the efficiency of the algorithm.The theoretical and numerical experiments show that all the new algorithms can preserve the details of the images well and avoid the staircase effects.