24,358 research outputs found
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
Spatial Compressive Sensing for MIMO Radar
We study compressive sensing in the spatial domain to achieve target
localization, specifically direction of arrival (DOA), using multiple-input
multiple-output (MIMO) radar. A sparse localization framework is proposed for a
MIMO array in which transmit and receive elements are placed at random. This
allows for a dramatic reduction in the number of elements needed, while still
attaining performance comparable to that of a filled (Nyquist) array. By
leveraging properties of structured random matrices, we develop a bound on the
coherence of the resulting measurement matrix, and obtain conditions under
which the measurement matrix satisfies the so-called isotropy property. The
coherence and isotropy concepts are used to establish uniform and non-uniform
recovery guarantees within the proposed spatial compressive sensing framework.
In particular, we show that non-uniform recovery is guaranteed if the product
of the number of transmit and receive elements, MN (which is also the number of
degrees of freedom), scales with K(log(G))^2, where K is the number of targets
and G is proportional to the array aperture and determines the angle
resolution. In contrast with a filled virtual MIMO array where the product MN
scales linearly with G, the logarithmic dependence on G in the proposed
framework supports the high-resolution provided by the virtual array aperture
while using a small number of MIMO radar elements. In the numerical results we
show that, in the proposed framework, compressive sensing recovery algorithms
are capable of better performance than classical methods, such as beamforming
and MUSIC.Comment: To appear in IEEE Transactions on Signal Processin
Adaptive Non-uniform Compressive Sampling for Time-varying Signals
In this paper, adaptive non-uniform compressive sampling (ANCS) of
time-varying signals, which are sparse in a proper basis, is introduced. ANCS
employs the measurements of previous time steps to distribute the sensing
energy among coefficients more intelligently. To this aim, a Bayesian inference
method is proposed that does not require any prior knowledge of importance
levels of coefficients or sparsity of the signal. Our numerical simulations
show that ANCS is able to achieve the desired non-uniform recovery of the
signal. Moreover, if the signal is sparse in canonical basis, ANCS can reduce
the number of required measurements significantly.Comment: 6 pages, 8 figures, Conference on Information Sciences and Systems
(CISS 2017) Baltimore, Marylan
Quantized Compressive K-Means
The recent framework of compressive statistical learning aims at designing
tractable learning algorithms that use only a heavily compressed
representation-or sketch-of massive datasets. Compressive K-Means (CKM) is such
a method: it estimates the centroids of data clusters from pooled, non-linear,
random signatures of the learning examples. While this approach significantly
reduces computational time on very large datasets, its digital implementation
wastes acquisition resources because the learning examples are compressed only
after the sensing stage. The present work generalizes the sketching procedure
initially defined in Compressive K-Means to a large class of periodic
nonlinearities including hardware-friendly implementations that compressively
acquire entire datasets. This idea is exemplified in a Quantized Compressive
K-Means procedure, a variant of CKM that leverages 1-bit universal quantization
(i.e. retaining the least significant bit of a standard uniform quantizer) as
the periodic sketch nonlinearity. Trading for this resource-efficient signature
(standard in most acquisition schemes) has almost no impact on the clustering
performances, as illustrated by numerical experiments
Pushing towards the Limit of Sampling Rate: Adaptive Chasing Sampling
Measurement samples are often taken in various monitoring applications. To
reduce the sensing cost, it is desirable to achieve better sensing quality
while using fewer samples. Compressive Sensing (CS) technique finds its role
when the signal to be sampled meets certain sparsity requirements. In this
paper we investigate the possibility and basic techniques that could further
reduce the number of samples involved in conventional CS theory by exploiting
learning-based non-uniform adaptive sampling.
Based on a typical signal sensing application, we illustrate and evaluate the
performance of two of our algorithms, Individual Chasing and Centroid Chasing,
for signals of different distribution features. Our proposed learning-based
adaptive sampling schemes complement existing efforts in CS fields and do not
depend on any specific signal reconstruction technique. Compared to
conventional sparse sampling methods, the simulation results demonstrate that
our algorithms allow less number of samples for accurate signal
reconstruction and achieve up to smaller signal reconstruction error
under the same noise condition.Comment: 9 pages, IEEE MASS 201
On the SNR Variability in Noisy Compressed Sensing
Compressed sensing (CS) is a sampling paradigm that allows to simultaneously
measure and compress signals that are sparse or compressible in some domain.
The choice of a sensing matrix that carries out the measurement has a defining
impact on the system performance and it is often advocated to draw its elements
randomly. It has been noted that in the presence of input (signal) noise, the
application of the sensing matrix causes SNR degradation due to the noise
folding effect. In fact, it might also result in the variations of the output
SNR in compressive measurements over the support of the input signal,
potentially resulting in unexpected non-uniform system performance. In this
work, we study the impact of a distribution from which the elements of a
sensing matrix are drawn on the spread of the output SNR. We derive analytic
expressions for several common types of sensing matrices and show that the SNR
spread grows with the decrease of the number of measurements. This makes its
negative effect especially pronounced for high compression rates that are often
of interest in CS.Comment: 4 pages + reference
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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