12,133 research outputs found
Operational Rate-Distortion Performance of Single-source and Distributed Compressed Sensing
We consider correlated and distributed sources without cooperation at the
encoder. For these sources, we derive the best achievable performance in the
rate-distortion sense of any distributed compressed sensing scheme, under the
constraint of high--rate quantization. Moreover, under this model we derive a
closed--form expression of the rate gain achieved by taking into account the
correlation of the sources at the receiver and a closed--form expression of the
average performance of the oracle receiver for independent and joint
reconstruction. Finally, we show experimentally that the exploitation of the
correlation between the sources performs close to optimal and that the only
penalty is due to the missing knowledge of the sparsity support as in (non
distributed) compressed sensing. Even if the derivation is performed in the
large system regime, where signal and system parameters tend to infinity,
numerical results show that the equations match simulations for parameter
values of practical interest.Comment: To appear in IEEE Transactions on Communication
Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks
A model, called the linear transform network (LTN), is proposed to analyze
the compression and estimation of correlated signals transmitted over directed
acyclic graphs (DAGs). An LTN is a DAG network with multiple source and
receiver nodes. Source nodes transmit subspace projections of random correlated
signals by applying reduced-dimension linear transforms. The subspace
projections are linearly processed by multiple relays and routed to intended
receivers. Each receiver applies a linear estimator to approximate a subset of
the sources with minimum mean squared error (MSE) distortion. The model is
extended to include noisy networks with power constraints on transmitters. A
key task is to compute all local compression matrices and linear estimators in
the network to minimize end-to-end distortion. The non-convex problem is solved
iteratively within an optimization framework using constrained quadratic
programs (QPs). The proposed algorithm recovers as special cases the regular
and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the
distortion region of multi-source, multi-receiver networks are given for linear
coding based on convex relaxations. Cut-set lower bounds are also given for any
coding strategy based on information theory. The distortion region and
compression-estimation tradeoffs are illustrated for different communication
demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal
Processin
Compressive Source Separation: Theory and Methods for Hyperspectral Imaging
With the development of numbers of high resolution data acquisition systems
and the global requirement to lower the energy consumption, the development of
efficient sensing techniques becomes critical. Recently, Compressed Sampling
(CS) techniques, which exploit the sparsity of signals, have allowed to
reconstruct signal and images with less measurements than the traditional
Nyquist sensing approach. However, multichannel signals like Hyperspectral
images (HSI) have additional structures, like inter-channel correlations, that
are not taken into account in the classical CS scheme. In this paper we exploit
the linear mixture of sources model, that is the assumption that the
multichannel signal is composed of a linear combination of sources, each of
them having its own spectral signature, and propose new sampling schemes
exploiting this model to considerably decrease the number of measurements
needed for the acquisition and source separation. Moreover, we give theoretical
lower bounds on the number of measurements required to perform reconstruction
of both the multichannel signal and its sources. We also proposed optimization
algorithms and extensive experimentation on our target application which is
HSI, and show that our approach recovers HSI with far less measurements and
computational effort than traditional CS approaches.Comment: 32 page
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