Fast Regularization of Matrix-Valued Images

Augmented-lagrangian Regularization of Matrix-valued Maps

We propose a novel framework for fast regularization of matrix-valued images. The resulting algorithms allow a unified treatment for a broad set of matrix groups and manifolds. Using an augmented-Lagrangian technique, we formulate a fast and highly parallel algorithm for matrixvalued image regularization. We demonstrate the applicability of the framework for various problems, such as motion ana...

Curvature-Preserving Regularization of Multi-valued Images Using PDE's

We are interested in diffusion PDE’s for smoothing multi-valued images in an anisotropic manner. By pointing out the pros and cons of existing tensor-driven regularization methods, we introduce a new constrained diffusion PDE that regularizes image data while taking curvatures of image structures into account. Our method has a direct link with a continuous formulation of the Line Integral Convo...

Diffusion and Regularization of Vector- and Matrix-Valued Images

Evaluation of the Regularization Algorithm to Decorrelation of Covariance Matrix of Float Ambiguity in Fast Resolution of GPS Ambiguity Parameters

Precise positioning in Real Time Kinematic (RTK) applications depends on the accurate resolution of the phase ambiguities. In RTK positioning, ambiguity parameters are highly correlated, especially when the positioning rate is high. Consequently, application of de-correlation techniques for the accurate resolution of ambiguities is inevitable. Phase ambiguity as positioning observations by the ...

Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation

In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...