2,639 research outputs found
Sparse Distributed Learning Based on Diffusion Adaptation
This article proposes diffusion LMS strategies for distributed estimation
over adaptive networks that are able to exploit sparsity in the underlying
system model. The approach relies on convex regularization, common in
compressive sensing, to enhance the detection of sparsity via a diffusive
process over the network. The resulting algorithms endow networks with learning
abilities and allow them to learn the sparse structure from the incoming data
in real-time, and also to track variations in the sparsity of the model. We
provide convergence and mean-square performance analysis of the proposed method
and show under what conditions it outperforms the unregularized diffusion
version. We also show how to adaptively select the regularization parameter.
Simulation results illustrate the advantage of the proposed filters for sparse
data recovery.Comment: to appear in IEEE Trans. on Signal Processing, 201
On the Performance Bound of Sparse Estimation with Sensing Matrix Perturbation
This paper focusses on the sparse estimation in the situation where both the
the sensing matrix and the measurement vector are corrupted by additive
Gaussian noises. The performance bound of sparse estimation is analyzed and
discussed in depth. Two types of lower bounds, the constrained Cram\'{e}r-Rao
bound (CCRB) and the Hammersley-Chapman-Robbins bound (HCRB), are discussed. It
is shown that the situation with sensing matrix perturbation is more complex
than the one with only measurement noise. For the CCRB, its closed-form
expression is deduced. It demonstrates a gap between the maximal and nonmaximal
support cases. It is also revealed that a gap lies between the CCRB and the MSE
of the oracle pseudoinverse estimator, but it approaches zero asymptotically
when the problem dimensions tend to infinity. For a tighter bound, the HCRB,
despite of the difficulty in obtaining a simple expression for general sensing
matrix, a closed-form expression in the unit sensing matrix case is derived for
a qualitative study of the performance bound. It is shown that the gap between
the maximal and nonmaximal cases is eliminated for the HCRB. Numerical
simulations are performed to verify the theoretical results in this paper.Comment: 32 pages, 8 Figures, 1 Tabl
Sub-Nyquist Sampling: Bridging Theory and Practice
Sampling theory encompasses all aspects related to the conversion of
continuous-time signals to discrete streams of numbers. The famous
Shannon-Nyquist theorem has become a landmark in the development of digital
signal processing. In modern applications, an increasingly number of functions
is being pushed forward to sophisticated software algorithms, leaving only
those delicate finely-tuned tasks for the circuit level.
In this paper, we review sampling strategies which target reduction of the
ADC rate below Nyquist. Our survey covers classic works from the early 50's of
the previous century through recent publications from the past several years.
The prime focus is bridging theory and practice, that is to pinpoint the
potential of sub-Nyquist strategies to emerge from the math to the hardware. In
that spirit, we integrate contemporary theoretical viewpoints, which study
signal modeling in a union of subspaces, together with a taste of practical
aspects, namely how the avant-garde modalities boil down to concrete signal
processing systems. Our hope is that this presentation style will attract the
interest of both researchers and engineers in the hope of promoting the
sub-Nyquist premise into practical applications, and encouraging further
research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin
Epigraphical Projection and Proximal Tools for Solving Constrained Convex Optimization Problems: Part I
We propose a proximal approach to deal with convex optimization problems involving nonlinear constraints. A large family of such constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For this class of constraints, the associated projection operator generally does not have a closed form. We circumvent this difficulty by splitting the lower level set into as many epigraphs as functions involved in the sum. A closed half-space constraint is also enforced, in order to limit the sum of the introduced epigraphical variables to the upper bound of the original lower level set. In this paper, we focus on a family of constraints involving linear transforms of l_1,p balls. Our main theoretical contribution is to provide closed form expressions of the epigraphical projections associated with the Euclidean norm and the sup norm. The proposed approach is validated in the context of image restoration with missing samples, by making use of TV-like constraints. Experiments show that our method leads to significant improvements in term of convergence speed over existing algorithms for solving similar constrained problems
Distributed UAV Swarm Augmented Wideband Spectrum Sensing Using Nyquist Folding Receiver
Distributed unmanned aerial vehicle (UAV) swarms are formed by multiple UAVs
with increased portability, higher levels of sensing capabilities, and more
powerful autonomy. These features make them attractive for many recent
applica-tions, potentially increasing the shortage of spectrum resources. In
this paper, wideband spectrum sensing augmented technology is discussed for
distributed UAV swarms to improve the utilization of spectrum. However, the
sub-Nyquist sampling applied in existing schemes has high hardware complexity,
power consumption, and low recovery efficiency for non-strictly sparse
conditions. Thus, the Nyquist folding receiver (NYFR) is considered for the
distributed UAV swarms, which can theoretically achieve full-band spectrum
detection and reception using a single analog-to-digital converter (ADC) at low
speed for all circuit components. There is a focus on the sensing model of two
multichannel scenarios for the distributed UAV swarms, one with a complete
functional receiver for the UAV swarm with RIS, and another with a
decentralized UAV swarm equipped with a complete functional receiver for each
UAV element. The key issue is to consider whether the application of RIS
technology will bring advantages to spectrum sensing and the data fusion
problem of decentralized UAV swarms based on the NYFR architecture. Therefore,
the property for multiple pulse reconstruction is analyzed through the
Gershgorin circle theorem, especially for very short pulses. Further, the block
sparse recovery property is analyzed for wide bandwidth signals. The proposed
technology can improve the processing capability for multiple signals and wide
bandwidth signals while reducing interference from folded noise and subsampled
harmonics. Experiment results show augmented spectrum sensing efficiency under
non-strictly sparse conditions
- …