Reconstruction of sparse wavelet signals from partial Fourier measurements

In this paper, we show that high-dimensional sparse wavelet signals of finite levels can be constructed from their partial Fourier measurements on a deterministic sampling set with cardinality about a multiple of signal sparsity

Stabilized Nearest Neighbor Classifier and Its Statistical Properties

The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same underlying population. In this paper, we introduce a general measure of classification instability (CIS) to quantify the sampling variability of the prediction made by a classification method. Interestingly, the asymptotic CIS of any weighted nearest neighbor classifier turns out to be proportional to the Euclidean norm of its weight vector. Based on this concise form, we propose a stabilized nearest neighbor (SNN) classifier, which distinguishes itself from other nearest neighbor classifiers, by taking the stability into consideration. In theory, we prove that SNN attains the minimax optimal convergence rate in risk, and a sharp convergence rate in CIS. The latter rate result is established for general plug-in classifiers under a low-noise condition. Extensive simulated and real examples demonstrate that SNN achieves a considerable improvement in CIS over existing nearest neighbor classifiers, with comparable classification accuracy. We implement the algorithm in a publicly available R package snn.Comment: 48 Pages, 11 Figures. To Appear in JASA--T&

Stable Large-Scale Perturbations in Interacting Dark-Energy Model

It is found that the evolutions of density perturbations on the super-Hubble scales are unstable in the model with dark-sector interaction $Q$ proportional to the energy density of cold dark matter (CDM) $\rho_m$ and constant equation of state parameter of dark energy $w_d$. In this paper, to avoid the instabilities, we suggest a new covariant model for the energy-momentum transfer between DE and CDM. Then we show that the the large-scale instabilities of curvature perturbations can be avoided in our model in the universe filled only by DE and CDM. Furthermore, by including the additional components of radiation and baryons, we calculate the dominant non-adiabatic modes in the radiation era and find that the modes grow in the power law with exponent at the order of unit.Comment: 14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1110.180

A fully end-to-end deep learning approach for real-time simultaneous 3D reconstruction and material recognition

This paper addresses the problem of simultaneous 3D reconstruction and material recognition and segmentation. Enabling robots to recognise different materials (concrete, metal etc.) in a scene is important for many tasks, e.g. robotic interventions in nuclear decommissioning. Previous work on 3D semantic reconstruction has predominantly focused on recognition of everyday domestic objects (tables, chairs etc.), whereas previous work on material recognition has largely been confined to single 2D images without any 3D reconstruction. Meanwhile, most 3D semantic reconstruction methods rely on computationally expensive post-processing, using Fully-Connected Conditional Random Fields (CRFs), to achieve consistent segmentations. In contrast, we propose a deep learning method which performs 3D reconstruction while simultaneously recognising different types of materials and labelling them at the pixel level. Unlike previous methods, we propose a fully end-to-end approach, which does not require hand-crafted features or CRF post-processing. Instead, we use only learned features, and the CRF segmentation constraints are incorporated inside the fully end-to-end learned system. We present the results of experiments, in which we trained our system to perform real-time 3D semantic reconstruction for 23 different materials in a real-world application. The run-time performance of the system can be boosted to around 10Hz, using a conventional GPU, which is enough to achieve real-time semantic reconstruction using a 30fps RGB-D camera. To the best of our knowledge, this work is the first real-time end-to-end system for simultaneous 3D reconstruction and material recognition.Comment: 8 pages, 7 figures, 4 table