标题： 通过松弛正则化去噪多色二维码和斯特费尔值数据 显示英文标题

标题： Denoising Multi-Color QR Codes and Stiefel-Valued Data by Relaxed Regularizations

摘要： 流形值数据的处理，在依赖于圆或球值颜色模型的颜色恢复任务中起着核心作用，在与特殊正交群相关的旋转或方向信息研究中，以及在高斯图像处理中，其中像素统计被解释为双曲面的值。特别是，为了去除这些类型的数据噪声，已经提出了几种总变分（TV）和Tikhonov型去噪模型的推广，这些模型结合了底层流形。最近，一种新颖且数值高效的去噪方法被引入，其中数据被嵌入到欧几里得环境空间中，非凸流形通过一系列正半定、固定秩矩阵进行编码，秩约束被放松以获得可以通过凸分析中的标准算法求解的凸化形式。本文的目的是将这种方法扩展到新的数据类型，如多二进制和Stiefel值数据。多二进制数据可以用来建模多颜色二维码，而Stiefel值数据出现在基于图像和视频的识别中。对于这两种新数据类型，我们提出了基于TV和Tikhonov的去噪模型，以及易于求解的凸化方法。所有推导出的方法都在概念验证的合成实验中进行了评估。 显示英文摘要

摘要： The handling of manifold-valued data, for instance, plays a central role in color restoration tasks relying on circle- or sphere-valued color models, in the study of rotational or directional information related to the special orthogonal group, and in Gaussian image processing, where the pixel statistics are interpreted as values on the hyperbolic sheet. Especially, to denoise these kind of data, there have been proposed several generalizations of total variation (TV) and Tikhonov-type denoising models incorporating the underlying manifolds. Recently, a novel, numerically efficient denoising approach has been introduced, where the data are embedded in an Euclidean ambient space, the non-convex manifolds are encoded by a series of positive semi-definite, fixed-rank matrices, and the rank constraint is relaxed to obtain a convexification that can be solved using standard algorithms from convex analysis. The aim of the present paper is to extent this approach to new kinds of data like multi-binary and Stiefel-valued data. Multi-binary data can, for instance, be used to model multi-color QR codes whereas Stiefel-valued data occur in image and video-based recognition. For both new data types, we propose TV- and Tikhonov-based denoising modelstogether with easy-to-solve convexification. All derived methods are evaluated on proof-of-concept, synthetic experiments.