10,736 research outputs found
Convolutional compressed sensing using deterministic sequences
This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain
Bayesian Estimation for Continuous-Time Sparse Stochastic Processes
We consider continuous-time sparse stochastic processes from which we have
only a finite number of noisy/noiseless samples. Our goal is to estimate the
noiseless samples (denoising) and the signal in-between (interpolation
problem).
By relying on tools from the theory of splines, we derive the joint a priori
distribution of the samples and show how this probability density function can
be factorized. The factorization enables us to tractably implement the maximum
a posteriori and minimum mean-square error (MMSE) criteria as two statistical
approaches for estimating the unknowns. We compare the derived statistical
methods with well-known techniques for the recovery of sparse signals, such as
the norm and Log (- relaxation) regularization
methods. The simulation results show that, under certain conditions, the
performance of the regularization techniques can be very close to that of the
MMSE estimator.Comment: To appear in IEEE TS
Xampling: Signal Acquisition and Processing in Union of Subspaces
We introduce Xampling, a unified framework for signal acquisition and
processing of signals in a union of subspaces. The main functions of this
framework are two. Analog compression that narrows down the input bandwidth
prior to sampling with commercial devices. A nonlinear algorithm then detects
the input subspace prior to conventional signal processing. A representative
union model of spectrally-sparse signals serves as a test-case to study these
Xampling functions. We adopt three metrics for the choice of analog
compression: robustness to model mismatch, required hardware accuracy and
software complexities. We conduct a comprehensive comparison between two
sub-Nyquist acquisition strategies for spectrally-sparse signals, the random
demodulator and the modulated wideband converter (MWC), in terms of these
metrics and draw operative conclusions regarding the choice of analog
compression. We then address lowrate signal processing and develop an algorithm
for that purpose that enables convenient signal processing at sub-Nyquist rates
from samples obtained by the MWC. We conclude by showing that a variety of
other sampling approaches for different union classes fit nicely into our
framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio
Modulated Unit-Norm Tight Frames for Compressed Sensing
In this paper, we propose a compressed sensing (CS) framework that consists
of three parts: a unit-norm tight frame (UTF), a random diagonal matrix and a
column-wise orthonormal matrix. We prove that this structure satisfies the
restricted isometry property (RIP) with high probability if the number of
measurements for -sparse signals of length
and if the column-wise orthonormal matrix is bounded. Some existing structured
sensing models can be studied under this framework, which then gives tighter
bounds on the required number of measurements to satisfy the RIP. More
importantly, we propose several structured sensing models by appealing to this
unified framework, such as a general sensing model with arbitrary/determinisic
subsamplers, a fast and efficient block compressed sensing scheme, and
structured sensing matrices with deterministic phase modulations, all of which
can lead to improvements on practical applications. In particular, one of the
constructions is applied to simplify the transceiver design of CS-based channel
estimation for orthogonal frequency division multiplexing (OFDM) systems.Comment: submitted to IEEE Transactions on Signal Processin
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