Abstract
The total variation model is widely used in image deblurring and denoising process with the features of protecting the image edge. However, this model usually causes some staircase effects. To overcome the shortcoming, combining the second-order total variation regularization and the total variation regularization, we propose a hybrid total variation model. The new improved model not only eliminates the staircase effect, but also well protects the edges of the image. The alternating direction method of multipliers (ADMM) is employed to solve the proposed model. Numerical results show that our proposed model can get more details and higher image visual quality than some current state-of-the-art methods.
Highlights
Image restoration mainly includes image deblurring and image denoising, which is one of the most fundamental problems in imaging science
The image restoration problem usually can be expressed in the following form: g = Hf + η, (1.1)
It is well known that the image restoration problem is usually an ill-posed problem
Summary
Image restoration mainly includes image deblurring and image denoising, which is one of the most fundamental problems in imaging science. To avoid the approach of penalty parameter to infinity, Chan et al [28] proposed the alternating direction method of multipliers (ADMM) to solve model (1.2). To overcome the shortcoming of the TV norm of f in model (1.2), Huang et al [29] proposed a fast total variation minimization method for image restoration as follows: min f ,u α1 f –u α2 u (1.3). To eliminate the staircase effect better and preserve edges very well in image processing, we combine the TV norm and second-order TV norm and introduce a new hybrid variational model as follows: α2. To overcome the disadvantage of numerical instability and large amount of calculations of the Chambolle projection algorithm, in this paper, we adopt the alternating direction multiplier method to solve subproblem (2.2).
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