Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data reconstruction, and so on. We propose a new model to recover a low-rank tensor by simultaneously performing low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An alternating minimization algorithm is applied to solve the model, along with two adaptive rank-adjusting strategies when the exact rank is not known.   Phase transition plots reveal that our algorithm can recover a variety of synthetic low-rank tensors from significantly fewer samples than the compared methods, which include a matrix completion method applied to tensor recovery and two state-of-the-art tensor completion methods. Further tests on real-world data show similar advantages. Although our model is non-convex, our algorithm performs consistently throughout the tests and gives better results than the compared methods, some of which are based on convex models. In addition, subsequence convergence of our algorithm can be established in the sense that any limit point of the iterates satisfies the KKT condtions.

Deep convolutional neural networks (CNNs) have contributed to the significant progress of the single-image super-resolution (SISR) field. However, the majority of existing CNN-based models maintain high performance with massive parameters and exceedingly deeper structures. Moreover, several algorithms essentially have underused the low-level features, thus causing relatively low performance. In this article, we address these problems by exploring two strategies based on novel local wider residual blocks (LWRBs) to effectively extract the image features for SISR. We propose a cascading residual network (CRN) that contains several locally sharing groups (LSGs), in which the cascading mechanism not only promotes the propagation of features and the gradient but also eases the model training. Besides, we present another enhanced residual network (ERN) for image resolution enhancement. ERN employs a dual global pathway structure that incorporates nonlocal operations to catch long-distance spatial features from the the original low-resolution (LR) input. To obtain the feature representation of the input at different scales, we further introduce a multiscale block (MSB) to directly detect low-level features from the LR image. The experimental results on four benchmark datasets have demonstrated that our models outperform most of the advanced methods while still retaining a reasonable number of parameters.

Point cloud processing is rapidly expanding the applicable scenarios in the industry. The surface normal is a fundamental feature for various point cloud processing tasks. Recently, deep supervised normal estimators outperform traditional normal estimation methods by adapting to dataset statistics. However, existing normal estimation methods mainly adopt hand-crafted features or complicated networks borrowed from other tasks and make less effort to design network models specifically for the problem. Instead of regressing the normal vector directly, we propose a simple deep network to estimate the normal vector based on a latent tangent space representation learned in the network. We call the network tangent represent learning network (TRNet). For each query point, the tangent space representation is a set of latent points spanning the tangent plane of it. The representation is generated using only the coordinates of its neighbors and regularized by a differentiable random sample consensus like component, which makes TRNet more compact and effective for normal estimation. We also design a compact multiscale network, denoted by multiresolution tangent representation learning network (MTRNet), to boost estimations from multiple TRNet trained with different fixed neighborhood size. Our TRNet and MTRNet perform favorably against state-of-the-art methods on synthesized data and real scenarios with far smaller model size.