A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Robust principal component analysis?
Journal of the ACM (JACM)
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
Camera calibration with lens distortion from low-rank textures
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Translation symmetry detection in a fronto-parallel view
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
De-noising by soft-thresholding
IEEE Transactions on Information Theory
TILT: Transform Invariant Low-Rank Textures
International Journal of Computer Vision
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Transform invariant low-rank textures (TILT) is a novel and powerful tool that can effectively rectify a rich class of low-rank textures in 3D scenes from 2D images despite significant deformation and corruption. The existing algorithm for solving TILT is based on the alternating direction method. It suffers from high computational cost and is not theoretically guaranteed to converge to a correct solution to the inner loop. In this paper, we propose a novel algorithm to speed up solving TILT, with guaranteed convergence for the inner loop. Our method is based on the recently proposed linearized alternating direction method with adaptive penalty. To further reduce computation, warm starts are also introduced to initialize the variables better and cut the cost on singular value decomposition. Extensive experimental results on both synthetic and real data demonstrate that this new algorithm works much more efficiently and robustly than the existing algorithm. It could be at least five times faster than the previous method.