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

TL;DR

This paper introduces a fast, convergent algorithm for Transform Invariant Low-rank Textures (TILT) that significantly reduces computation time and improves robustness, enabling more efficient rectification of low-rank textures in images.

Contribution

It proposes a novel linearized ADMM with adaptive penalty and warm starts for TILT, achieving guaranteed convergence and at least five times faster performance than previous methods.

Findings

At least five times faster than previous algorithms.

Demonstrates robustness on synthetic and real data.

Guarantees convergence of the proposed method.

Abstract

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 (ADM). It suffers from high computational cost and is not theoretically guaranteed to converge to a correct solution. In this paper, we propose a novel algorithm to speed up solving TILT, with guaranteed convergence. Our method is based on the recently proposed linearized alternating direction method with adaptive penalty (LADMAP). 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.