Tikhonov Regularization of Circle-Valued Signals

Tikhonov Regularization of Sphere-Valued Signals

It is common to have to process signals, whose values are points on the 3-D sphere. We consider a Tikhonov-type regularization model to smoothen or interpolate sphere-valued signals defined on arbitrary graphs. We propose a convex relaxation of this nonconvex problem as a semidefinite program, which is easy to solve numerically and is efficient in practice.

基于松弛Tikhonov正则化的球面与SO(3)值数据去噪

Denoising of Sphere- and SO(3)-Valued Data by Relaxed Tikhonov Regularization

该研究将圆值数据去噪的凸松弛Tikhonov正则化方法简化并推广至球面与SO(3)值数据，用凸分析标准算法求解，验证了方法的去噪效果与数值收敛性。

Convex regularization of discrete-valued inverse problems

This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex but nondifferentiable regularization term. This allows applying standard approaches to show well-posedness and convergence rates in Bregman distance. Using the specific properties of the regularization term, it can be shown that convergence (albeit without rates) actually holds pointwise. Furthermore, the resulting Tikhonov functional can be minimized effic…

通过松弛正则化对多色QR码和Stiefel值数据进行去噪

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

本文将一种基于松弛秩约束的高效去噪方法扩展至多二值和Stiefel值数据，提出了基于TV和Tikhonov的去噪模型及凸化方法，并通过合成实验验证了其有效性。

多参数Tikhonov正则化

Multi-Parameter Tikhonov Regularization

研究多惩罚项的多参数Tikhonov正则化，提出差异原则和平衡原则两种参数选择规则，建立理论结果并设计固定点算法，数值实验表明多参数模型优于单参数模型。

Tikhonov正则化系统的强收敛性与快速收敛率

Strong convergence and fast rates for systems with Tikhonov regularization

研究实希尔伯特空间中带Tikhonov正则化的二阶动力系统，通过消失阻尼和校正项实现轨迹向最小范数解的强收敛及快速收敛率，并将其应用于线性约束凸优化的原始对偶系统。