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

Navigation and control based on integral-uncertainty observer for unmanned jet aircraft

A nonlinear integral-uncertainty observer is presented, which can estimate the integral of measurement output signal and the uncertainty in system, synchronously. In order to be satisfied with the existing hardware computational environments and to select the parameters more easily, a simplified linear version of the nonlinear integral-uncertainty observer is also developed. The effectiveness of the proposed observers are verified through the numerical simulations and experiments: i) through the integral-uncertainty observers, the attitude angle and the uncertainties in attitude dynamics are estimated synchronously from the measurements of angular velocity, and the estimate results by the two observers are compared; ii) a control law is designed based on the observers to drive the jet aircraft to track a reference trajectory