scholarly journals A Telescopic Bregmanian Proximal Gradient Method Without the Global Lipschitz Continuity Assumption

2019 ◽  
Vol 182 (3) ◽  
pp. 851-884 ◽  
Author(s):  
Daniel Reem ◽  
Simeon Reich ◽  
Alvaro De Pierro
Keyword(s):  
Gradient Method ◽  
Lipschitz Continuity ◽  
Proximal Gradient Method ◽  
Continuity Assumption

Distributed proximal-gradient method for convex optimization with inequality constraints

2015 ◽  
Vol 56 ◽  
pp. 160 ◽  
Author(s):  
Jueyou Li ◽  
Changzhi Wu ◽  
Zhiyou Wu ◽  
Qiang Long ◽  
Xiangyu Wang
Keyword(s):  
Convex Optimization ◽  
Gradient Method ◽  
Inequality Constraints ◽  
Proximal Gradient Method

scholarly journals Learned Collaborative Stereo Refinement

2021 ◽  
Author(s):  
Patrick Knöbelreiter ◽  
Thomas Pock
Keyword(s):  
Structural Properties ◽  
Gradient Method ◽  
Color Image ◽  
Image Space ◽  
Activation Functions ◽  
Disparity Map ◽  
Proximal Gradient Method ◽  
Variational Structure ◽  
Disparity Maps ◽  
The Individual

AbstractIn this work, we propose a learning-based method to denoise and refine disparity maps. The proposed variational network arises naturally from unrolling the iterates of a proximal gradient method applied to a variational energy defined in a joint disparity, color, and confidence image space. Our method allows to learn a robust collaborative regularizer leveraging the joint statistics of the color image, the confidence map and the disparity map. Due to the variational structure of our method, the individual steps can be easily visualized, thus enabling interpretability of the method. We can therefore provide interesting insights into how our method refines and denoises disparity maps. To this end, we can visualize and interpret the learned filters and activation functions and prove the increased reliability of the predicted pixel-wise confidence maps. Furthermore, the optimization based structure of our refinement module allows us to compute eigen disparity maps, which reveal structural properties of our refinement module. The efficiency of our method is demonstrated on the publicly available stereo benchmarks Middlebury 2014 and Kitti 2015.

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