Few-view image reconstruction with fractional-order total variation

2014 ◽  
Vol 31 (5) ◽  
pp. 981 ◽  
Author(s):  
Yi Zhang ◽  
Weihua Zhang ◽  
Yinjie Lei ◽  
Jiliu Zhou
Author(s):  
Cong Pham ◽  
Thi Thu Tran ◽  
Minh Pham ◽  
Thanh Cong Nguyen

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.


Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 150
Author(s):  
Lijia Hou ◽  
Yali Qin ◽  
Huan Zheng ◽  
Zemin Pan ◽  
Jicai Mei ◽  
...  

Total variation often yields staircase artifacts in the smooth region of the image reconstruction. This paper proposes a hybrid high-order and fractional-order total variation with nonlocal regularization algorithm. The nonlocal means regularization is introduced to describe image structural prior information. By selecting appropriate weights in the fractional-order and high-order total variation coefficients, the proposed algorithm makes the fractional-order and the high-order total variation complement each other on image reconstruction. It can solve the problem of non-smooth in smooth areas when fractional-order total variation can enhance image edges and textures. In addition, it also addresses high-order total variation alleviates the staircase artifact produced by traditional total variation, still smooth the details of the image and the effect is not ideal. Meanwhile, the proposed algorithm suppresses painting-like effects caused by nonlocal means regularization. The Lagrange multiplier method and the alternating direction multipliers method are used to solve the regularization problem. By comparing with several state-of-the-art reconstruction algorithms, the proposed algorithm is more efficient. It does not only yield higher peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) but also retain abundant details and textures efficiently. When the measurement rate is 0.1, the gains of PSNR and SSIM are up to 1.896 dB and 0.048 dB respectively compared with total variation with nonlocal regularization (TV-NLR).


2021 ◽  
Vol 30 (01) ◽  
Author(s):  
Hui Chen ◽  
Yali Qin ◽  
Chenbo Feng ◽  
Hongliang Ren ◽  
Linlin Xue ◽  
...  

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.


IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 47698-47713 ◽  
Author(s):  
Zongrui Wu ◽  
Xi Chen ◽  
Wenxuan Shi ◽  
Liqiong Chen ◽  
Shiyong Hu

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