China 
Africa 
Explore chapters and articles related to this topic
Image Formation in Spectral Computed Tomography
Published in Katsuyuki Taguchi, Ira Blevis, Krzysztof Iniewski, Spectral, Photon Counting Computed Tomography, 2020
Simon Rit, Cyril Mory, Peter B. Noël
Some algorithms address the non-convexity using a primal-dual metric algorithm. Foygel Barber et al. developed the Mirrored Convex/Concave Optimization for Nonconvex Composite Functions (MOCCA) [18, 63], a primal-dual scheme derived from the Chambolle-Pock algorithm [11]. Tairi et al. [75] used a variable-metric primal algorithm [13].
The integrated acceleration of the Chambolle-Pock algorithm applied to constrained TV minimization in CT image reconstruction
Published in Inverse Problems in Science and Engineering, 2019
Zhiwei Qiao, Yining Zhu, Gage Redler, Shaojie Tang
ASD-POCS is designed according to the physical meaning of the optimization programme. It may not always guarantee convergence for the algorithm parameters are physically designed rather than mathematically derived though an appropriate parameters setting may arrive at convergence in most cases. Another potential disadvantage is that the convergence speed will be very slow when the image-solver has moved to the boundary of the data-tolerance-error-ball [2]. ADMM algorithm simplifies the process of the non-smooth ℓ1 norm by introducing a new variable, then use shrinkage operation to solve the ℓ1 norm minimization problem. The main disadvantage of ADMM is that there is a sub-optimization problem which has not close form. Chambolle-Pock algorithm framework is a powerful algorithm tool to solve various convex optimization programmes even if they are non-smooth [13].
Equivalent resolvents of Douglas-Rachford splitting and other operator splitting algorithms: a unified degenerate proximal point analysis
Published in Optimization, 2023
Taking the PDS structure (26) for instance, the t-update can be preconditioned as3: Thus, (26) becomes the well-known Chambolle-Pock algorithm [17,Algorithm 1]: The PPA form associated with (31) has recently been a standard result in [24,31,32,35,38,50,54]: from which, by Theorem 2.1-(ii), follows that the weak convergence of is guaranteed, if (which corresponds to a non-degenerate metric in (32)).