656 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
Compressive Sensing Using Iterative Hard Thresholding with Low Precision Data Representation: Theory and Applications
Modern scientific instruments produce vast amounts of data, which can
overwhelm the processing ability of computer systems. Lossy compression of data
is an intriguing solution, but comes with its own drawbacks, such as potential
signal loss, and the need for careful optimization of the compression ratio. In
this work, we focus on a setting where this problem is especially acute:
compressive sensing frameworks for interferometry and medical imaging. We ask
the following question: can the precision of the data representation be lowered
for all inputs, with recovery guarantees and practical performance? Our first
contribution is a theoretical analysis of the normalized Iterative Hard
Thresholding (IHT) algorithm when all input data, meaning both the measurement
matrix and the observation vector are quantized aggressively. We present a
variant of low precision normalized {IHT} that, under mild conditions, can
still provide recovery guarantees. The second contribution is the application
of our quantization framework to radio astronomy and magnetic resonance
imaging. We show that lowering the precision of the data can significantly
accelerate image recovery. We evaluate our approach on telescope data and
samples of brain images using CPU and FPGA implementations achieving up to a 9x
speed-up with negligible loss of recovery quality.Comment: 19 pages, 5 figures, 1 table, in IEEE Transactions on Signal
Processin
Exact Performance Analysis of the Oracle Receiver for Compressed Sensing Reconstruction
A sparse or compressible signal can be recovered from a certain number of
noisy random projections, smaller than what dictated by classic Shannon/Nyquist
theory. In this paper, we derive the closed-form expression of the mean square
error performance of the oracle receiver, knowing the sparsity pattern of the
signal. With respect to existing bounds, our result is exact and does not
depend on a particular realization of the sensing matrix. Moreover, our result
holds irrespective of whether the noise affecting the measurements is white or
correlated. Numerical results show a perfect match between equations and
simulations, confirming the validity of the result.Comment: To be published in ICASSP 2014 proceeding
The Pros and Cons of Compressive Sensing for Wideband Signal Acquisition: Noise Folding vs. Dynamic Range
Compressive sensing (CS) exploits the sparsity present in many signals to
reduce the number of measurements needed for digital acquisition. With this
reduction would come, in theory, commensurate reductions in the size, weight,
power consumption, and/or monetary cost of both signal sensors and any
associated communication links. This paper examines the use of CS in the design
of a wideband radio receiver in a noisy environment. We formulate the problem
statement for such a receiver and establish a reasonable set of requirements
that a receiver should meet to be practically useful. We then evaluate the
performance of a CS-based receiver in two ways: via a theoretical analysis of
its expected performance, with a particular emphasis on noise and dynamic
range, and via simulations that compare the CS receiver against the performance
expected from a conventional implementation. On the one hand, we show that
CS-based systems that aim to reduce the number of acquired measurements are
somewhat sensitive to signal noise, exhibiting a 3dB SNR loss per octave of
subsampling, which parallels the classic noise-folding phenomenon. On the other
hand, we demonstrate that since they sample at a lower rate, CS-based systems
can potentially attain a significantly larger dynamic range. Hence, we conclude
that while a CS-based system has inherent limitations that do impose some
restrictions on its potential applications, it also has attributes that make it
highly desirable in a number of important practical settings
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