Completing Low-Rank Matrices with Corrupted Samples from Few Coefficients in General Basis

Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods mostly concentrate on recovering a low-rank matrix from few corrupted coefficients w.r.t. standard basis, which, however, does not apply to more general basis, e.g., Fourier basis. In this paper, we prove that the range space of an $m\times n$ matrix with rank $r$ can be exactly recovered from few coefficients w.r.t. general basis, though $r$ and the number of corrupted samples are both as high as $O(\min\{m,n\}/\log^3 (m+n))$. Our model covers previous ones as special cases, and robust MC can recover the intrinsic matrix with a higher rank. Moreover, we suggest a universal choice of the regularization parameter, which is $\lambda=1/\sqrt{\log n}$. By our $\ell_{2,1}$ filtering algorithm, which has theoretical guarantees, we can further reduce the computational cost of our model. As an application, we also find that the solutions to extended robust Low-Rank Representation and to our extended robust MC are mutually expressible, so both our theory and algorithm can be applied to the subspace clustering problem with missing values under certain conditions. Experiments verify our theories.Comment: To appear in IEEE Transactions on Information Theor

Inner and Inter Label Propagation: Salient Object Detection in the Wild

In this paper, we propose a novel label propagation based method for saliency detection. A key observation is that saliency in an image can be estimated by propagating the labels extracted from the most certain background and object regions. For most natural images, some boundary superpixels serve as the background labels and the saliency of other superpixels are determined by ranking their similarities to the boundary labels based on an inner propagation scheme. For images of complex scenes, we further deploy a 3-cue-center-biased objectness measure to pick out and propagate foreground labels. A co-transduction algorithm is devised to fuse both boundary and objectness labels based on an inter propagation scheme. The compactness criterion decides whether the incorporation of objectness labels is necessary, thus greatly enhancing computational efficiency. Results on five benchmark datasets with pixel-wise accurate annotations show that the proposed method achieves superior performance compared with the newest state-of-the-arts in terms of different evaluation metrics.Comment: The full version of the TIP 2015 publicatio

Face Recognition from Sequential Sparse 3D Data via Deep Registration

Previous works have shown that face recognition with high accurate 3D data is more reliable and insensitive to pose and illumination variations. Recently, low-cost and portable 3D acquisition techniques like ToF(Time of Flight) and DoE based structured light systems enable us to access 3D data easily, e.g., via a mobile phone. However, such devices only provide sparse(limited speckles in structured light system) and noisy 3D data which can not support face recognition directly. In this paper, we aim at achieving high-performance face recognition for devices equipped with such modules which is very meaningful in practice as such devices will be very popular. We propose a framework to perform face recognition by fusing a sequence of low-quality 3D data. As 3D data are sparse and noisy which can not be well handled by conventional methods like the ICP algorithm, we design a PointNet-like Deep Registration Network(DRNet) which works with ordered 3D point coordinates while preserving the ability of mining local structures via convolution. Meanwhile we develop a novel loss function to optimize our DRNet based on the quaternion expression which obviously outperforms other widely used functions. For face recognition, we design a deep convolutional network which takes the fused 3D depth-map as input based on AMSoftmax model. Experiments show that our DRNet can achieve rotation error 0.95{\deg} and translation error 0.28mm for registration. The face recognition on fused data also achieves rank-1 accuracy 99.2% , FAR-0.001 97.5% on Bosphorus dataset which is comparable with state-of-the-art high-quality data based recognition performance.Comment: To be appeared in ICB201

Coastal Upwelling Off the China Coasts

Upwelling is an important oceanographic phenomenon that brings cooler and nutrient-rich water upward to the surface, facilitating the growth of phytoplankton and other primary producers, which results in high levels of primary productivity and hence fishery production. This chapter presents a review of recent studies on six major upwelling regions along the China coasts, with a focus on the eastern and southeastern coasts of mainland China, based on in situ measurements, satellite observations and numerical simulations. These upwelling regions result primarily from the summer monsoon winds, though other mechanisms, such as river discharge, baroclinicity, topography, tides, and the presence of mean current, may also be in play. In this review, their impacts on local biogeochemical processes are briefly summarized. Also discussed are their possible responses to the globally changing climate

A comparative study of Grid and Natural sentences effects on Normal-to-Lombard conversion

Grid sentence is commonly used for studying the Lombard effect and Normal-to-Lombard conversion. However, it's unclear if Normal-to-Lombard models trained on grid sentences are sufficient for improving natural speech intelligibility in real-world applications. This paper presents the recording of a parallel Lombard corpus (called Lombard Chinese TIMIT, LCT) extracting natural sentences from Chinese TIMIT. Then We compare natural and grid sentences in terms of Lombard effect and Normal-to-Lombard conversion using LCT and Enhanced MAndarin Lombard Grid corpus (EMALG). Through a parametric analysis of the Lombard effect, We find that as the noise level increases, both natural sentences and grid sentences exhibit similar changes in parameters, but in terms of the increase of the alpha ratio, grid sentences show a greater increase. Following a subjective intelligibility assessment across genders and Signal-to-Noise Ratios, the StarGAN model trained on EMALG consistently outperforms the model trained on LCT in terms of improving intelligibility. This superior performance may be attributed to EMALG's larger alpha ratio increase from normal to Lombard speech