scholarly journals Efficient Iterative Regularization Method for Total Variation-Based Image Restoration

Electronics ◽  
2022 ◽  
Vol 11 (2) ◽  
pp. 258
Author(s):  
Ge Ma ◽  
Ziwei Yan ◽  
Zhifu Li ◽  
Zhijia Zhao
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Method ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Split Bregman ◽  
Iterative Regularization ◽  
Tv Regularization ◽  
Fidelity Term ◽  
Restoration Effect

Total variation (TV) regularization has received much attention in image restoration applications because of its advantages in denoising and preserving details. A common approach to address TV-based image restoration is to design a specific algorithm for solving typical cost function, which consists of conventional ℓ2 fidelity term and TV regularization. In this work, a novel objective function and an efficient algorithm are proposed. Firstly, a pseudoinverse transform-based fidelity term is imposed on TV regularization, and a closely-related optimization problem is established. Then, the split Bregman framework is used to decouple the complex inverse problem into subproblems to reduce computational complexity. Finally, numerical experiments show that the proposed method can obtain satisfactory restoration results with fewer iterations. Combined with the restoration effect and efficiency, this method is superior to the competitive algorithm. Significantly, the proposed method has the advantage of a simple solving structure, which can be easily extended to other image processing applications.

scholarly journals An Iterative Regularization Method for Total Variation-Based Image Restoration

2005 ◽  
Vol 4 (2) ◽  
pp. 460-489 ◽  
Author(s):  
Stanley Osher ◽  
Martin Burger ◽  
Donald Goldfarb ◽  
Jinjun Xu ◽  
Wotao Yin
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Method ◽  
Iterative Regularization

scholarly journals Performance of relaxed iterative methods for image deblurring problems

2019 ◽  
Vol 13 ◽  
pp. 174830261986173 ◽  
Author(s):  
Jae H Yun
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Total Variation ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Image Deblurring ◽  
Total Variation Regularization ◽  
L1 Norm ◽  
Split Bregman ◽  
Relaxation Parameters

In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good preconditioners and near optimal relaxation parameters which are essential factors for fast convergence rate and computational efficiency of relaxation iterative methods. We next study efficient applications of relaxation iterative methods to Split Bregman method and the fixed point method for solving the L1-norm or total variation regularization problems. Lastly, we provide numerical experiments for four types of image deblurring problems to evaluate the efficiency of relaxation iterative methods by comparing their performances with those of Krylov subspace iterative methods. Numerical experiments show that the proposed techniques for finding preconditioners and near optimal relaxation parameters of relaxation iterative methods work well for image deblurring problems. For the L1-norm and total variation regularization problems, Split Bregman and fixed point methods using relaxation iterative methods perform quite well in terms of both peak signal to noise ratio values and execution time as compared with those using Krylov subspace methods.

A Non-linear Inverse Problem in Estimating the Reaction Rate Function for an Annular-Bed Reactor

2014 ◽  
Vol 12 (1) ◽  
pp. 271-283
Author(s):  
Cheng-Hung Huang ◽  
Bo-Yi Li
Keyword(s):  
Regularization Method ◽  
Measurement Errors ◽  
Numerical Experiments ◽  
Reaction Rate ◽  
Prior Information ◽  
Functional Form ◽  
Rate Function ◽  
Function Estimation ◽  
Iterative Regularization ◽  
Cpu Time

Abstract The conjugate gradient method, or iterative regularization method, based inverse algorithm is utilized in this work to predict the unknown concentration-dependent reaction rate function for an annular-bed reactor (ABR) using interior measurements of concentration distributions. Since no prior information on the functional form of unknown reaction rate is available, it can be classified as function estimation for the inverse calculation. The validity and accuracy of this inverse ABR problem are examined using the simulated exact and inexact concentration measurements in the numerical experiments. Results show that the estimation of the concentration-dependent reaction rate function can be obtained within a very short CPU time on an Intel Xeon Core 2 2.00 GHz personal computer, and reliable estimations can still be obtained when measurement errors are considered.

scholarly journals Combined total variation of first and fractional orders for Poisson noise removal in digital images

2021 ◽  
pp. 10-19
Author(s):  
Cong Pham ◽  
Thi Thu Tran ◽  
Minh Pham ◽  
Thanh Cong Nguyen
Keyword(s):  
Image Reconstruction ◽  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Optimization Problem ◽  
Poisson Noise ◽  
Experimental Results ◽  
First Order ◽  
Proposed Model ◽  
Total Variation Model

Introduction: Many methods have been proposed to handle the image restoration problem with Poisson noise. A popular approach to Poissonian image reconstruction is the one based on Total Variation. This method can provide significantly sharp edges and visually fine images, but it results in piecewise-constant regions in the resulting images. Purpose: Developing an adaptive total variation-based model for the reconstruction of images contaminated by Poisson noise, and an algorithm for solving the optimization problem. Results: We proposed an effective way to restore images degraded by Poisson noise. Using the Bayesian framework, we proposed an adaptive model based on a combination of first-order total variation and fractional order total variation. The first-order total variation model is efficient for suppressing the noise and preserving the keen edges simultaneously. However, the first-order total variation method usually causes artifact problems in the obtained results. To avoid this drawback, we can use high-order total variation models, one of which is the fractional-order total variation-based model for image restoration. In the fractional-order total variation model, the derivatives have an order greater than or equal to one. It leads to the convenience of computation with a compact discrete form. However, methods based on the fractional-order total variation may cause image blurring. Thus, the proposed model incorporates the advantages of two total variation regularization models, having a significant effect on the edge-preserving image restoration. In order to solve the considered optimization problem, the Split Bregman method is used. Experimental results are provided, demonstrating the effectiveness of the proposed method.  Practical relevance: The proposed method allows you to restore Poissonian images preserving their edges. The presented numerical simulation demonstrates the competitive performance of the model proposed for image reconstruction. Discussion: From the experimental results, we can see that the proposed algorithm is effective in suppressing noise and preserving the image edges. However, the weighted parameters in the proposed model were not automatically selected at each iteration of the proposed algorithm. This requires additional research.

scholarly journals A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization

2020 ◽  
Vol 12 (21) ◽  
pp. 3541
Author(s):  
Saori Takeyama ◽  
Shunsuke Ono ◽  
Itsuo Kumazawa
Keyword(s):  
Convex Optimization ◽  
Image Restoration ◽  
Optimization Problem ◽  
Hyperspectral Image ◽  
Optimization Problems ◽  
Low Rank ◽  
Optimization Approach ◽  
Regularization Term ◽  
Data Fidelity ◽  
Fidelity Term

We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problems, consisting of a regularization term(s) and a data-fidelity term(s). The methods have to handle a regularization term(s) and a data-fidelity term(s) simultaneously in one objective function; therefore, we need to carefully control the hyperparameter(s) that balances these terms. However, the setting of such hyperparameters is often a troublesome task because their suitable values depend strongly on the regularization terms adopted and the noise intensities on a given observation. Our proposed method is formulated as a convex optimization problem, utilizing a novel hybrid regularization technique named Hybrid Spatio-Spectral Total Variation (HSSTV) and incorporating data-fidelity as hard constraints. HSSTV has a strong noise and artifact removal ability while avoiding oversmoothing and spectral distortion, without combining other regularizations such as low-rank modeling-based ones. In addition, the constraint-type data-fidelity enables us to translate the hyperparameters that balance between regularization and data-fidelity to the upper bounds of the degree of data-fidelity that can be set in a much easier manner. We also develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to efficiently solve the optimization problem. We illustrate the advantages of the proposed method over various HS image restoration methods through comprehensive experiments, including state-of-the-art ones.

scholarly journals Iterative Nonlocal Total Variation Regularization Method for Image Restoration

PLoS ONE ◽  
2013 ◽  
Vol 8 (6) ◽  
pp. e65865 ◽  
Author(s):  
Huanyu Xu ◽  
Quansen Sun ◽  
Nan Luo ◽  
Guo Cao ◽  
Deshen Xia
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Method ◽  
Total Variation Regularization ◽  
Nonlocal Total Variation

scholarly journals An Efficient Variational Method for Image Restoration

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jun Liu ◽  
Ting-Zhu Huang ◽  
Xiao-Guang Lv ◽  
Si Wang
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Signal To Noise Ratio ◽  
Similarity Index ◽  
Total Variation Regularization ◽  
Split Bregman ◽  
Split Bregman Iteration ◽  
Imaging Science ◽  
Constrained Minimization Problem ◽  
Structure Similarity Index

Image restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In this paper, we consider a constrained minimization problem with double total variation regularization terms. To solve this problem, we employ the split Bregman iteration method and the Chambolle’s algorithm. The convergence property of the algorithm is established. The numerical results demonstrate the effectiveness of the proposed method in terms of peak signal-to-noise ratio (PSNR) and the structure similarity index (SSIM).

scholarly journals SIMRES-TV: NOISE AND RESIDUAL SIMILARITY FOR PARAMETER ESTIMATION IN TOTAL VARIATION

2021 ◽  
Vol XLIV-2/W1-2021 ◽  
pp. 171-176
Author(s):  
V. B. S. Prasath ◽  
N. N. Hien ◽  
D. N. H. Thanh ◽  
S. Dvoenko
Keyword(s):  
Image Processing ◽  
Parameter Estimation ◽  
Image Restoration ◽  
Total Variation ◽  
Regularization Parameter ◽  
Noise Levels ◽  
Split Bregman ◽  
Edge Preserving ◽  
Restoration Scheme ◽  
Split Bregman Algorithm

Abstract. Image restoration with regularization models is very popular in the image processing literature. Total variation (TV) is one of the important edge preserving regularization models used, however, to obtain optimal restoration results the regularization parameter needs to be set appropriately. We propose here a new parameter estimation approach for total variation based image restoration. By utilizing known noise levels we compute the regularization parameter by reducing the similarity between residual and noise variances. We use the split Bregman algorithm for the total variation along with this automatic parameter estimation step to obtain a very fast restoration scheme. Experimental results indicate the proposed parameter estimation obtained better denoised images and videos in terms of PSNR and SSIM measures and the computational overload is less compared with other approaches.

scholarly journals Fast Total-Variation Image Deconvolution with Adaptive Parameter Estimation via Split Bregman Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chuan He ◽  
Changhua Hu ◽  
Wei Zhang ◽  
Biao Shi ◽  
Xiaoxiang Hu
Keyword(s):  
Total Variation ◽  
Regularization Parameter ◽  
Difficult Problem ◽  
Image Deconvolution ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Edge Preservation ◽  
Adaptive Parameter ◽  
Tv Regularization ◽  
Blurred Image

The total-variation (TV) regularization has been widely used in image restoration domain, due to its attractive edge preservation ability. However, the estimation of the regularization parameter, which balances the TV regularization term and the data-fidelity term, is a difficult problem. In this paper, based on the classical split Bregman method, a new fast algorithm is derived to simultaneously estimate the regularization parameter and to restore the blurred image. In each iteration, the regularization parameter is refreshed conveniently in a closed form according to Morozov’s discrepancy principle. Numerical experiments in image deconvolution show that the proposed algorithm outperforms some state-of-the-art methods both in accuracy and in speed.

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