Truncated Nuclear Norm Minimization for Image Restoration Based On Iterative Support Detection

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation and the low-rank matrix recovery problem is solved through minimization of the nuclear norm regularized problem. However, a major limitation of nuclear norm minimization is that all the singular values are simultaneously minimized and the rank may not be well approximated \cite{hu2012fast}. Correspondingly, in this paper, we propose a new multi-stage algorithm, which makes use of the concept of Truncated Nuclear Norm Regularization (TNNR) proposed in \citep{hu2012fast} and Iterative Support Detection (ISD) proposed in \citep{wang2010sparse} to overcome the above limitation. Besides matrix completion problems considered in \citep{hu2012fast}, the proposed method can be also extended to the general low-rank matrix recovery problems. Extensive experiments well validate the superiority of our new algorithms over other state-of-the-art methods

Nonlinear signal-correction observer and application to UAV navigation

A nonlinear signal-correction observer (NSCO) is presented for signals correction and estimation, which not only can reject the position measurement error, but also the unknown velocity can be estimated, in spite of the existence of large position measurement error and intense stochastic non-Gaussian noise. For this method, the position signal is not required to be bounded. The NSCO is developed for position/acceleration integration, and it is applied to an unmanned aerial vehicle (UAV) navigation: Based on the NSCO, the position and flying velocity of quadrotor UAV are estimated. An experiment is conducted to demonstrate the effectiveness of the proposed method

Comparative Research on China and Taiwan’s Legal Systems: From the View of the Agent Right of Daily Household Matters

The agent right of household matters is one of an important aspect of personal rights and also a personal interest that cannot be ignored. As early as in late Qing dynasty, Chinese legal workers had paid attention on the agent right of household matters. Related legislations can be found in Civil Law Draft of Qing Dynasty (Family Chapter) and the Civil Law Draft of the Republic of China. Due to the social traditions at that time, these laws just stipulated wife’s agent right but not the husband’s. Until in the 1930 Civil Law issued by Nanking National Government, the provisions governing spouses’ rights were transplanted from foreign civil laws and the system of agent right of household matters was first time established. However, because China followed Soviet’s legal mode after the founding of the state, the agent right of household matters was replaced by marital property regime. Ever since that time Taiwan and Chinese mainland’s legal provisions on this right differs. The main aim of this paper is to provide some useful research for settling continuous disputes in modern society through comparative study on China and Taiwan’s agent right of household matters legislation emphasis, subjects, limitations, and burdens