Many geometry processing applications are sensitive to noise and sharp features. Although there are a number of works on detecting noise and sharp features in the literature, they are heuristic. On one hand, traditional denoising methods use filtering operators to remove noise, however, they may blur sharp features and shrink the object. On the other hand, noise makes detection of features, which relies on computation of differential properties, unreliable and unstable. Therefore, detecting noise and features on discrete surfaces still remains challenging.In this article, we present an approach for decoupling noise and features on 3D shapes. Our approach consists of two phases. In the first phase, a base mesh is estimated from the input noisy data by a global Laplacian regularization denoising scheme. The estimated base mesh is guaranteed to asymptotically converge to the true underlying surface with probability one as the sample size goes to infinity. In the second phase, an 1 -analysis compressed sensing optimization is proposed to recover sharp features from the residual between base mesh and input mesh. This is based on our discovery that sharp features can be sparsely represented in some coherent dictionary which is constructed by the pseudo-inverse matrix of the Laplacian of the shape. The features are recovered from the residual in a progressive way. Theoretical analysis and experimental results show that our approach can reliably and robustly remove noise and extract sharp features on 3D shapes.

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We report the observation of multi-component dipole and vortex vector solitons composed of eight coexisting four-wave mixing (FWM) signals in two-level atomic system. The formation and stability of the multi-component dipole and vortex vector solitons are observed via changing the experiment parameters, including the frequency detuning, powers, and spatial configuration of the involved beams and the temperature of the medium. The transformation between modulated vortex solitons and rotating dipole solitons is observed at different frequency detunings. The interaction forces between different components of vector solitons are also investigated.

A brain-computer interface (BCI) is a communication approach that permits cerebral activity to control computers or external devices. Brain electrical activity recorded with electroencephalography (EEG) is most commonly used for BCI. Noise-assisted multivariate empirical mode decomposition (NA-MEMD) is a data-driven time-frequency analysis method that can be applied to nonlinear and nonstationary EEG signals for BCI data processing. However, because white Gaussian noise occupies a broad range of frequencies, some redundant components are introduced. To solve this leakage problem, in this study, we propose using a sinusoidal assisted signal that occupies the same frequency ranges as the original signals to improve MEMD performance. To verify the effectiveness of the proposed sinusoidal signal assisted MEMD (SA-MEMD) method, we compared the decomposition performances of MEMD, NA-MEMD, and the proposed SA-MEMD using synthetic signals and a real-world BCI dataset. The spectral decomposition results indicate that the proposed SA-MEMD can avoid the generation of redundant components and over decomposition, thus, substantially reduce the mode mixing and misalignment that occurs in MEMD and NA-MEMD. Moreover, using SA-MEMD as a signal preprocessing method instead of MEMD or NA-MEMD can significantly improve BCI classification accuracy and reduce calculation time, which indicates that SA-MEMD is a powerful spectral decomposition method for BCI.

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