2,217 research outputs found
From Sparse Signals to Sparse Residuals for Robust Sensing
One of the key challenges in sensor networks is the extraction of information
by fusing data from a multitude of distinct, but possibly unreliable sensors.
Recovering information from the maximum number of dependable sensors while
specifying the unreliable ones is critical for robust sensing. This sensing
task is formulated here as that of finding the maximum number of feasible
subsystems of linear equations, and proved to be NP-hard. Useful links are
established with compressive sampling, which aims at recovering vectors that
are sparse. In contrast, the signals here are not sparse, but give rise to
sparse residuals. Capitalizing on this form of sparsity, four sensing schemes
with complementary strengths are developed. The first scheme is a convex
relaxation of the original problem expressed as a second-order cone program
(SOCP). It is shown that when the involved sensing matrices are Gaussian and
the reliable measurements are sufficiently many, the SOCP can recover the
optimal solution with overwhelming probability. The second scheme is obtained
by replacing the initial objective function with a concave one. The third and
fourth schemes are tailored for noisy sensor data. The noisy case is cast as a
combinatorial problem that is subsequently surrogated by a (weighted) SOCP.
Interestingly, the derived cost functions fall into the framework of robust
multivariate linear regression, while an efficient block-coordinate descent
algorithm is developed for their minimization. The robust sensing capabilities
of all schemes are verified by simulated tests.Comment: Under review for publication in the IEEE Transactions on Signal
Processing (revised version
Stable Camera Motion Estimation Using Convex Programming
We study the inverse problem of estimating n locations (up to
global scale, translation and negation) in from noisy measurements of a
subset of the (unsigned) pairwise lines that connect them, that is, from noisy
measurements of for some pairs (i,j) (where the
signs are unknown). This problem is at the core of the structure from motion
(SfM) problem in computer vision, where the 's represent camera locations
in . The noiseless version of the problem, with exact line measurements,
has been considered previously under the general title of parallel rigidity
theory, mainly in order to characterize the conditions for unique realization
of locations. For noisy pairwise line measurements, current methods tend to
produce spurious solutions that are clustered around a few locations. This
sensitivity of the location estimates is a well-known problem in SfM,
especially for large, irregular collections of images.
In this paper we introduce a semidefinite programming (SDP) formulation,
specially tailored to overcome the clustering phenomenon. We further identify
the implications of parallel rigidity theory for the location estimation
problem to be well-posed, and prove exact (in the noiseless case) and stable
location recovery results. We also formulate an alternating direction method to
solve the resulting semidefinite program, and provide a distributed version of
our formulation for large numbers of locations. Specifically for the camera
location estimation problem, we formulate a pairwise line estimation method
based on robust camera orientation and subspace estimation. Lastly, we
demonstrate the utility of our algorithm through experiments on real images.Comment: 40 pages, 12 figures, 6 tables; notation and some unclear parts
updated, some typos correcte
Collaborative Spectrum Sensing from Sparse Observations in Cognitive Radio Networks
Spectrum sensing, which aims at detecting spectrum holes, is the precondition
for the implementation of cognitive radio (CR). Collaborative spectrum sensing
among the cognitive radio nodes is expected to improve the ability of checking
complete spectrum usage. Due to hardware limitations, each cognitive radio node
can only sense a relatively narrow band of radio spectrum. Consequently, the
available channel sensing information is far from being sufficient for
precisely recognizing the wide range of unoccupied channels. Aiming at breaking
this bottleneck, we propose to apply matrix completion and joint sparsity
recovery to reduce sensing and transmitting requirements and improve sensing
results. Specifically, equipped with a frequency selective filter, each
cognitive radio node senses linear combinations of multiple channel information
and reports them to the fusion center, where occupied channels are then decoded
from the reports by using novel matrix completion and joint sparsity recovery
algorithms. As a result, the number of reports sent from the CRs to the fusion
center is significantly reduced. We propose two decoding approaches, one based
on matrix completion and the other based on joint sparsity recovery, both of
which allow exact recovery from incomplete reports. The numerical results
validate the effectiveness and robustness of our approaches. In particular, in
small-scale networks, the matrix completion approach achieves exact channel
detection with a number of samples no more than 50% of the number of channels
in the network, while joint sparsity recovery achieves similar performance in
large-scale networks.Comment: 12 pages, 11 figure
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