Fast Regularization of Matrix-Valued Images

摘要

Regularization of matrix-valued data is important in many fields, such as medical imaging, motion analysis and scene understanding, where accurate estimation of diffusion tensors or rigid motions is crucial for higher-level computer vision tasks. In this chapter we describe a novel method for efficient regularization of matrix- and group-valued images. Using the augmented Lagrangian framework we separate the total-variation regularization of matrix-valued images into a regularization and projection steps, both of which are fast and parallelizable. Furthermore we extend our method to a high-order regularization scheme for matrix-valued functions. We demonstrate the effectiveness of our method for denoising of several group-valued image types, with data in SO(n), SE(n), and SPD(n), and discuss its convergence properties.