Linearized Alternating Direction Method with Adaptive Penalty and Warm Starts for Fast Solving Transform Invariant Low-Rank Textures

摘要

Transform Invariant Low-rank Textures (TILT) is a novel and powerful toolthat can effectively rectify a rich class of low-rank textures in 3D scenesfrom 2D images despite significant deformation and corruption. The existingalgorithm for solving TILT is based on the alternating direction method (ADM).It suffers from high computational cost and is not theoretically guaranteed toconverge to a correct solution. In this paper, we propose a novel algorithm tospeed up solving TILT, with guaranteed convergence. Our method is based on therecently proposed linearized alternating direction method with adaptive penalty(LADMAP). To further reduce computation, warm starts are also introduced toinitialize the variables better and cut the cost on singular valuedecomposition. Extensive experimental results on both synthetic and real datademonstrate that this new algorithm works much more efficiently and robustlythan the existing algorithm. It could be at least five times faster than theprevious method.