A Nonlocal Denoising Algorithm for Manifold-Valued Images Using Second Order Statistics

07/28/2016
by   Friederike Laus, et al.
0

Nonlocal patch-based methods, in particular the Bayes' approach of Lebrun, Buades and Morel (2013), are considered as state-of-the-art methods for denoising (color) images corrupted by white Gaussian noise of moderate variance. This paper is the first attempt to generalize this technique to manifold-valued images. Such images, for example images with phase or directional entries or with values in the manifold of symmetric positive definite matrices, are frequently encountered in real-world applications. Generalizing the normal law to manifolds is not canonical and different attempts have been considered. Here we focus on a straightforward intrinsic model and discuss the relation to other approaches for specific manifolds. We reinterpret the Bayesian approach of Lebrun et al. (2013) in terms of minimum mean squared error estimation, which motivates our definition of a corresponding estimator on the manifold. With this estimator at hand we present a nonlocal patch-based method for the restoration of manifold-valued images. Various proof of concept examples demonstrate the potential of the proposed algorithm.

READ FULL TEXT

page 15

page 24

page 25

page 26

page 27

page 29

page 30

research
07/04/2020

An Empirical Bayes Approach to Shrinkage Estimation on the Manifold of Symmetric Positive-Definite Matrices

The James-Stein estimator is an estimator of the multivariate normal mea...
research
12/05/2017

Manifold-valued Image Generation with Wasserstein Adversarial Networks

Unsupervised image generation has recently received an increasing amount...
research
12/30/2013

Total variation regularization for manifold-valued data

We consider total variation minimization for manifold valued data. We pr...
research
03/30/2020

ManifoldNorm: Extending normalizations on Riemannian Manifolds

Many measurements in computer vision and machine learning manifest as no...
research
06/22/2020

C-SURE: Shrinkage Estimator and Prototype Classifier for Complex-Valued Deep Learning

The James-Stein (JS) shrinkage estimator is a biased estimator that capt...
research
10/19/2021

Hermite multiwavelets for manifold-valued data

In this paper we present a construction of interpolatory Hermite multiwa...
research
01/31/2023

Multi-Fidelity Covariance Estimation in the Log-Euclidean Geometry

We introduce a multi-fidelity estimator of covariance matrices that empl...

Please sign up or login with your details

Forgot password? Click here to reset