Image denoising based on nonconvex anisotropic total-variation regularization

To avoid the staircase artifacts, an adaptive image denoising model is proposed by the weighted combination of Tikhonov regularization and total variation regularization. In our model, Tikhonov regularization and total variation regularization can be adaptively selected based on the gradient information of the image. When the pixels belong to the smooth regions, Tikhonov regularization is adopted, which can eliminate the staircase artifacts. When the pixels locate at the edges, total variation regularization is selected, which can preserve the edges. We employ the split Bregman method to solve our model. Experimental results demonstrate that our model can obtain better performance than those of other models.

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Multidirectional Anisotropic Total Variation and Its Application in the Tomography of the Surrounding Rock of Coal Mining Faces

Shock and Vibration ◽

10.1155/2021/1138620 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Bo Chen ◽

Guowei Zhu ◽

Zhenqiang Yang

Keyword(s):

Coal Mining ◽

Total Variation ◽

Regularization Method ◽

Surrounding Rock ◽

Total Variation Regularization ◽

Ct Reconstruction ◽

Traveltime Tomography ◽

Transmitted Waves ◽

Mining Face ◽

Anisotropic Total Variation

The computed tomography (CT) reconstruction algorithm is one of the crucial components of the CT system. To date, total variation (TV) has been widely used in CT reconstruction algorithms. Although TV utilizes the a priori information of the longitudinal and lateral gradient sparsity of an image, it introduces some staircase artifacts. To overcome the current limitations of TV and improve imaging quality, we propose a multidirectional anisotropic total variation (MATV) that uses multidirectional gradient information. The surrounding rock of coal mining faces uses principles of tomography similar to those of medical X-rays. The velocity distribution for the surrounding rock can be obtained by the first-arrival traveltime tomography of the transmitted waves in the coal mining face. Combined with the geological data, we can interpret the geological hazards in the coal mining face. To perform traveltime tomography, we first established the objective function of the first-arrival traveltime tomography of the transmitted waves based on the MATV regularization and then used the split Bregman method to solve the objective function. The simulated data and real data show that the MATV regularization method proposed in this paper can better maintain the boundaries of geological anomalies and reduce the artifacts compared with the isotropic total variation regularization method and the anisotropic total variation regularization method. Furthermore, this approach describes the distribution of geological anomalies more accurately and effectively and improves imaging accuracy.

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Step phase reconstruction using an anisotropic total variation regularization method in a diffraction phase microscopy

Applied Optics ◽

10.1364/ao.58.007189 ◽

2019 ◽

Vol 58 (26) ◽

pp. 7189 ◽

Cited By ~ 3

Author(s):

Allaparthi Venkata Satya Vithin ◽

Sreeprasad Ajithaprasad ◽

Gannavarpu Rajshekhar

Keyword(s):

Total Variation ◽

Regularization Method ◽

Total Variation Regularization ◽

Phase Reconstruction ◽

Phase Microscopy ◽

Anisotropic Total Variation

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Data-driven multichannel seismic impedance inversion with anisotropic total variation regularization

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2017-0024 ◽

2018 ◽

Vol 26 (2) ◽

pp. 229-241 ◽

Cited By ~ 4

Author(s):

Dehua Wang ◽

Jinghuai Gao ◽

Hongan Zhou

Keyword(s):

Total Variation ◽

Seismic Data ◽

Reservoir Characterization ◽

Data Driven ◽

Total Variation Regularization ◽

Split Bregman ◽

Seismic Reflection Data ◽

Reflection Data ◽

Impedance Inversion ◽

Anisotropic Total Variation

AbstractAcoustic impedance (AI) inversion is a desirable tool to extract rock-physical properties from recorded seismic data. It plays an important role in seismic interpretation and reservoir characterization. When one of recursive inversion schemes is employed to obtain the AI, the spatial coherency of the estimated reflectivity section may be damaged through the trace-by-trace processing. Meanwhile, the results are sensitive to noise in the data or inaccuracies in the generated reflectivity function. To overcome the above disadvantages, in this paper, we propose a data-driven inversion scheme to directly invert the AI from seismic reflection data. We first explain in principle that the anisotropic total variation (ATV) regularization is more suitable for inverting the impedance with sharp interfaces than the total variation (TV) regularization, and then establish the nonlinear objective function of the AI model by using anisotropic total variation (ATV) regularization. Next, we solve the nonlinear impedance inversion problem via the alternating split Bregman iterative algorithm. Finally, we illustrate the performance of the proposed method and its robustness to noise with synthetic and real seismic data examples by comparing with the conventional methods.

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