886,168 research outputs found
Partially Linear Estimation with Application to Sparse Signal Recovery From Measurement Pairs
We address the problem of estimating a random vector X from two sets of
measurements Y and Z, such that the estimator is linear in Y. We show that the
partially linear minimum mean squared error (PLMMSE) estimator does not require
knowing the joint distribution of X and Y in full, but rather only its
second-order moments. This renders it of potential interest in various
applications. We further show that the PLMMSE method is minimax-optimal among
all estimators that solely depend on the second-order statistics of X and Y. We
demonstrate our approach in the context of recovering a signal, which is sparse
in a unitary dictionary, from noisy observations of it and of a filtered
version of it. We show that in this setting PLMMSE estimation has a clear
computational advantage, while its performance is comparable to
state-of-the-art algorithms. We apply our approach both in static and dynamic
estimation applications. In the former category, we treat the problem of image
enhancement from blurred/noisy image pairs, where we show that PLMMSE
estimation performs only slightly worse than state-of-the art algorithms, while
running an order of magnitude faster. In the dynamic setting, we provide a
recursive implementation of the estimator and demonstrate its utility in the
context of tracking maneuvering targets from position and acceleration
measurements.Comment: 13 pages, 5 figure
3D Face Reconstruction by Learning from Synthetic Data
Fast and robust three-dimensional reconstruction of facial geometric
structure from a single image is a challenging task with numerous applications.
Here, we introduce a learning-based approach for reconstructing a
three-dimensional face from a single image. Recent face recovery methods rely
on accurate localization of key characteristic points. In contrast, the
proposed approach is based on a Convolutional-Neural-Network (CNN) which
extracts the face geometry directly from its image. Although such deep
architectures outperform other models in complex computer vision problems,
training them properly requires a large dataset of annotated examples. In the
case of three-dimensional faces, currently, there are no large volume data
sets, while acquiring such big-data is a tedious task. As an alternative, we
propose to generate random, yet nearly photo-realistic, facial images for which
the geometric form is known. The suggested model successfully recovers facial
shapes from real images, even for faces with extreme expressions and under
various lighting conditions.Comment: The first two authors contributed equally to this wor
A Near-linear Time Approximation Algorithm for Angle-based Outlier Detection in High-dimensional Data
Outlier mining in d-dimensional point sets is a fundamental and well studied data mining task due to its variety of ap-plications. Most such applications arise in high-dimensional domains. A bottleneck of existing approaches is that implicit or explicit assessments on concepts of distance or nearest neighbor are deteriorated in high-dimensional data. Follow-ing up on the work of Kriegel et al. (KDD ’08), we inves-tigate the use of angle-based outlier factor in mining high-dimensional outliers. While their algorithm runs in cubic time (with a quadratic time heuristic), we propose a novel random projection-based technique that is able to estimate the angle-based outlier factor for all data points in time near-linear in the size of the data. Also, our approach is suitable to be performed in parallel environment to achieve a parallel speedup. We introduce a theoretical analysis of the quality of approximation to guarantee the reliability of our estima-tion algorithm. The empirical experiments on synthetic and real world data sets demonstrate that our approach is effi-cient and scalable to very large high-dimensional data sets
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