scholarly journals Split Bregman Iteration Algorithm for Image Deblurring Using Fourth-Order Total Bounded Variation Regularization Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yi Xu ◽  
Ting-Zhu Huang ◽  
Jun Liu ◽  
Xiao-Guang Lv
Keyword(s):  
Bounded Variation ◽  
Fourth Order ◽  
Convergence Property ◽  
Iteration Algorithm ◽  
Bregman Iteration ◽  
Split Bregman ◽  
Split Bregman Iteration ◽  
Proposed Model ◽  
Optimum Solution

We propose a fourth-order total bounded variation regularization model which could reduce undesirable effects effectively. Based on this model, we introduce an improved split Bregman iteration algorithm to obtain the optimum solution. The convergence property of our algorithm is provided. Numerical experiments show the more excellent visual quality of the proposed model compared with the second-order total bounded variation model which is proposed by Liu and Huang (2010).

scholarly journals TV+TV2Regularization with Nonconvex Sparseness-Inducing Penalty for Image Restoration

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chengwu Lu ◽  
Hua Huang
Keyword(s):  
Bregman Iteration ◽  
Split Bregman ◽  
Split Bregman Iteration ◽  
High Quality Image ◽  
Proposed Model ◽  
Quality Image ◽  
Robustness To Noise ◽  
Sharp Edges ◽  
Geometrical Information ◽  
Restoration Method

In order to restore the high quality image, we propose a compound regularization method which combines a new higher-order extension of total variation (TV+TV2) and a nonconvex sparseness-inducing penalty. Considering the presence of varying directional features in images, we employ the shearlet transform to preserve the abundant geometrical information of the image. The nonconvex sparseness-inducing penalty approach increases robustness to noise and image nonsparsity. In what follows, we present the numerical solution of the proposed model by employing the split Bregman iteration and a novelp-shrinkage operator. And finally, we perform numerical experiments for image denoising, image deblurring, and image reconstructing from incomplete spectral samples. The experimental results demonstrate the efficiency of the proposed restoration method for preserving the structure details and the sharp edges of image.

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