scholarly journals Hybrid High-Order and Fractional-Order Total Variation with Nonlocal Regularization for Compressive Sensing Image Reconstruction

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 150
Author(s):  
Lijia Hou ◽  
Yali Qin ◽  
Huan Zheng ◽  
Zemin Pan ◽  
Jicai Mei ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Total Variation ◽  
Fractional Order ◽  
Signal To Noise Ratio ◽  
Structural Similarity ◽  
High Order ◽  
Reconstruction Algorithms ◽  
Nonlocal Means ◽  
Smooth Region ◽  
Nonlocal Regularization

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).

scholarly journals Adaptive Weighted High Frequency Iterative Algorithm for Fractional-Order Total Variation with Nonlocal Regularization for Image Reconstruction

Electronics ◽  
2020 ◽  
Vol 9 (7) ◽  
pp. 1103
Author(s):  
Hui Chen ◽  
Yali Qin ◽  
Hongliang Ren ◽  
Liping Chang ◽  
Yingtian Hu ◽  
...  
Keyword(s):  
Total Variation ◽  
Iterative Algorithm ◽  
Fractional Order ◽  
High Frequency ◽  
Structural Information ◽  
Similarity Index ◽  
Structural Similarity ◽  
Nonlocal Means ◽  
Nonlocal Regularization ◽  
Staircase Artifacts

We propose an adaptive weighted high frequency iterative algorithm for a fractional-order total variation (FrTV) approach with nonlocal regularization to alleviate image deterioration and to eliminate staircase artifacts, which result from the total variation (TV) method. The high frequency gradients are reweighted in iterations adaptively when we decompose the image into high and low frequency components using the pre-processing technique. The nonlocal regularization is introduced into our method based on nonlocal means (NLM) filtering, which contains prior image structural information to suppress staircase artifacts. An alternating direction multiplier method (ADMM) is used to solve the problem combining reweighted FrTV and nonlocal regularization. Experimental results show that both the peak signal-to-noise ratios (PSNR) and structural similarity index (SSIM) of reconstructed images are higher than those achieved by the other four methods at various sampling ratios less than 25%. At 5% sampling ratios, the gains of PSNR and SSIM are up to 1.63 dB and 0.0114 from ten images compared with reweighted total variation with nuclear norm regularization (RTV-NNR). The improved approach preserves more texture details and has better visual effects, especially at low sampling ratios, at the cost of taking more time.

A compensating total variation image denoising model combining L1 and L2 norm

2020 ◽  
pp. 002072092092330
Author(s):  
Liqiong Zhang ◽  
Min Li ◽  
Xiaohua Qiu
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Structural Information ◽  
Signal To Noise Ratio ◽  
Similarity Index ◽  
Structural Similarity ◽  
Isotropic Diffusion ◽  
Model Combining ◽  
L2 Norm ◽  
Staircase Effect

To overcome the “staircase effect” while preserving the structural information such as image edges and textures quickly and effectively, we propose a compensating total variation image denoising model combining L1 and L2 norm. A new compensating regular term is designed, which can perform anisotropic and isotropic diffusion in image denoising, thus making up for insufficient diffusion in the total variation model. The algorithm first uses local standard deviation to distinguish neighborhood types. Then, the anisotropic diffusion based on L1 norm plays the role of edge protection in the strong edge region. The anisotropic and the isotropic diffusion simultaneously exist in the smooth region, so that the weak textures can be protected while overcoming the “staircase effect” effectively. The simulation experiments show that this method can effectively improve the peak signal-to-noise ratio and obtain the higher structural similarity index and the shorter running time.

scholarly journals A Soft-Threshold Filtering Approach for Tomography Reconstruction from a Limited Number of Projections with Bilateral Edge Preservation

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2346
Author(s):  
Tiago Wirtti ◽  
Evandro Salles
Keyword(s):  
Objective Function ◽  
Total Variation ◽  
Signal To Noise Ratio ◽  
Similarity Index ◽  
Structural Similarity ◽  
Edge Preservation ◽  
Edge Preserving ◽  
Reconstruction Process ◽  
Regularization Term ◽  
Computational Performance

In X-ray tomography image reconstruction, one of the most successful approaches involves a statistical approach with l 2 norm for fidelity function and some regularization function with l p norm, 1 < p < 2 . Among them stands out, both for its results and the computational performance, a technique that involves the alternating minimization of an objective function with l 2 norm for fidelity and a regularization term that uses discrete gradient transform (DGT) sparse transformation minimized by total variation (TV). This work proposes an improvement to the reconstruction process by adding a bilateral edge-preserving (BEP) regularization term to the objective function. BEP is a noise reduction method and has the purpose of adaptively eliminating noise in the initial phase of reconstruction. The addition of BEP improves optimization of the fidelity term and, as a consequence, improves the result of DGT minimization by total variation. For reconstructions with a limited number of projections (low-dose reconstruction), the proposed method can achieve higher peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM) results because it can better control the noise in the initial processing phase.

Few-view image reconstruction combining total variation and a high-order norm

2013 ◽  
Vol 23 (3) ◽  
pp. 249-255 ◽  
Author(s):  
Yi Zhang ◽  
Wei-Hua Zhang ◽  
Hu Chen ◽  
Meng-Long Yang ◽  
Tai-Yong Li ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Total Variation ◽  
High Order

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.

Clinical low dose CT image reconstruction using high-order total variation techniques

2010 ◽  
Author(s):  
Synho Do ◽  
W. Clem Karl ◽  
Mannudeep K. Kalra ◽  
Thomas J. Brady ◽  
Homer Pien
Keyword(s):  
Image Reconstruction ◽  
Total Variation ◽  
Low Dose ◽  
High Order ◽  
Ct Image ◽  
Low Dose Ct ◽  
Ct Image Reconstruction ◽  
Variation Techniques

scholarly journals Deep Learning-Based Fast TOF-PET Image Reconstruction Using Direction Information

2021 ◽  
Author(s):  
Kibo Ote ◽  
Fumio Hashimoto
Keyword(s):  
Deep Learning ◽  
Image Reconstruction ◽  
Image Quality ◽  
Signal To Noise Ratio ◽  
Structural Similarity ◽  
Fast Time ◽  
Reconstruction Method ◽  
Direction Information ◽  
Pet Image Reconstruction ◽  
Tof Pet

Abstract Deep learning has attracted attention for positron emission tomography (PET) image reconstruction task, however, it remains necessary to further improve the image quality. In this study, we propose a novel CNN-based fast time-of-flight PET (TOF-PET) image reconstruction method to fully utilize the direction information of coincidence events. The proposed method inputs view-grouped histo-images into a 3D CNN as a multi-channel image to use the direction information of coincidence events. We evaluated the proposed method using Monte Carlo simulation data obtained from a digital brain phantom. Compared to the case without it, when using direction information, the peak signal-to-noise ratio and structural similarity were improved by 1.2 dB and 0.02, at a coincidence time resolution of 300 ps. The calculation times of the proposed method were significantly faster than the conventional iterative reconstruction. These results indicate that the proposed method improves both the speed and image quality of TOF-PET image reconstruction.

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