965 research outputs found
Joint Sparse Recovery Method for Compressed Sensing with Structured Dictionary Mismatches
In traditional compressed sensing theory, the dictionary matrix is given a
priori, whereas in real applications this matrix suffers from random noise and
fluctuations. In this paper we consider a signal model where each column in the
dictionary matrix is affected by a structured noise. This formulation is common
in direction-of-arrival (DOA) estimation of off-grid targets, encountered in
both radar systems and array processing. We propose to use joint sparse signal
recovery to solve the compressed sensing problem with structured dictionary
mismatches and also give an analytical performance bound on this joint sparse
recovery. We show that, under mild conditions, the reconstruction error of the
original sparse signal is bounded by both the sparsity and the noise level in
the measurement model. Moreover, we implement fast first-order algorithms to
speed up the computing process. Numerical examples demonstrate the good
performance of the proposed algorithm, and also show that the joint-sparse
recovery method yields a better reconstruction result than existing methods. By
implementing the joint sparse recovery method, the accuracy and efficiency of
DOA estimation are improved in both passive and active sensing cases.Comment: Submitted on Aug 27th, 2013(Revise on Feb 16th, 2014, Accepted on
July 21th, 2014
Super-Resolution Compressed Sensing: A Generalized Iterative Reweighted L2 Approach
Conventional compressed sensing theory assumes signals have sparse
representations in a known, finite dictionary. Nevertheless, in many practical
applications such as direction-of-arrival (DOA) estimation and line spectral
estimation, the sparsifying dictionary is usually characterized by a set of
unknown parameters in a continuous domain. To apply the conventional compressed
sensing technique to such applications, the continuous parameter space has to
be discretized to a finite set of grid points, based on which a "presumed
dictionary" is constructed for sparse signal recovery. Discretization, however,
inevitably incurs errors since the true parameters do not necessarily lie on
the discretized grid. This error, also referred to as grid mismatch, may lead
to deteriorated recovery performance or even recovery failure. To address this
issue, in this paper, we propose a generalized iterative reweighted L2 method
which jointly estimates the sparse signals and the unknown parameters
associated with the true dictionary. The proposed algorithm is developed by
iteratively decreasing a surrogate function majorizing a given objective
function, resulting in a gradual and interweaved iterative process to refine
the unknown parameters and the sparse signal. A simple yet effective scheme is
developed for adaptively updating the regularization parameter that controls
the tradeoff between the sparsity of the solution and the data fitting error.
Extension of the proposed algorithm to the multiple measurement vector scenario
is also considered. Numerical results show that the proposed algorithm achieves
a super-resolution accuracy and presents superiority over other existing
methods.Comment: arXiv admin note: text overlap with arXiv:1401.431
Super-Resolution Compressed Sensing: An Iterative Reweighted Algorithm for Joint Parameter Learning and Sparse Signal Recovery
In many practical applications such as direction-of-arrival (DOA) estimation
and line spectral estimation, the sparsifying dictionary is usually
characterized by a set of unknown parameters in a continuous domain. To apply
the conventional compressed sensing to such applications, the continuous
parameter space has to be discretized to a finite set of grid points.
Discretization, however, incurs errors and leads to deteriorated recovery
performance. To address this issue, we propose an iterative reweighted method
which jointly estimates the unknown parameters and the sparse signals.
Specifically, the proposed algorithm is developed by iteratively decreasing a
surrogate function majorizing a given objective function, which results in a
gradual and interweaved iterative process to refine the unknown parameters and
the sparse signal. Numerical results show that the algorithm provides superior
performance in resolving closely-spaced frequency components
Multiple Measurement Vectors Problem: A Decoupling Property and its Applications
We study a Compressed Sensing (CS) problem known as Multiple Measurement
Vectors (MMV) problem, which arises in joint estimation of multiple signal
realizations when the signal samples have a common (joint) sparse support over
a fixed known dictionary. Although there is a vast literature on the analysis
of MMV, it is not yet fully known how the number of signal samples and their
statistical correlations affects the performance of the joint estimation in
MMV. Moreover, in many instances of MMV the underlying sparsifying dictionary
may not be precisely known, and it is still an open problem to quantify how the
dictionary mismatch may affect the estimation performance.
In this paper, we focus on -norm regularized least squares
(-LS) as a well-known and widely-used MMV algorithm in the
literature. We prove an interesting decoupling property for -LS,
where we show that it can be decomposed into two phases: i) use all the signal
samples to estimate the signal covariance matrix (coupled phase), ii) plug in
the resulting covariance estimate as the true covariance matrix into the
Minimum Mean Squared Error (MMSE) estimator to reconstruct each signal sample
individually (decoupled phase). As a consequence of this decomposition, we are
able to provide further insights on the performance of -LS for MMV.
In particular, we address how the signal correlations and dictionary mismatch
affects its performance. Moreover, we show that by using the decoupling
property one can obtain a variety of MMV algorithms with performances even
better than that of -LS. We also provide numerical simulations to
validate our theoretical results.Comment: 9 pages, 4 figure
Gridless Quadrature Compressive Sampling with Interpolated Array Technique
Quadrature compressive sampling (QuadCS) is a sub-Nyquist sampling scheme for
acquiring in-phase and quadrature (I/Q) components in radar. In this scheme,
the received intermediate frequency (IF) signals are expressed as a linear
combination of time-delayed and scaled replicas of the transmitted waveforms.
For sparse IF signals on discrete grids of time-delay space, the QuadCS can
efficiently reconstruct the I/Q components from sub-Nyquist samples. In
practice, the signals are characterized by a set of unknown time-delay
parameters in a continuous space. Then conventional sparse signal
reconstruction will deteriorate the QuadCS reconstruction performance. This
paper focuses on the reconstruction of the I/Q components with continuous delay
parameters. A parametric spectrum-matched dictionary is defined, which sparsely
describes the IF signals in the frequency domain by delay parameters and gain
coefficients, and the QuadCS system is reexamined under the new dictionary.
With the inherent structure of the QuadCS system, it is found that the
estimation of delay parameters can be decoupled from that of sparse gain
coefficients, yielding a beamspace direction-of-arrival (DOA) estimation
formulation with a time-varying beamforming matrix. Then an interpolated
beamspace DOA method is developed to perform the DOA estimation. An optimal
interpolated array is established and sufficient conditions to guarantee the
successful estimation of the delay parameters are derived. With the estimated
delays, the gain coefficients can be conveniently determined by solving a
linear least-squares problem. Extensive simulations demonstrate the superior
performance of the proposed algorithm in reconstructing the sparse signals with
continuous delay parameters.Comment: 34 pages, 11 figure
Sparse Bayesian learning with uncertainty models and multiple dictionaries
Sparse Bayesian learning (SBL) has emerged as a fast and competitive method
to perform sparse processing. The SBL algorithm, which is developed using a
Bayesian framework, approximately solves a non-convex optimization problem
using fixed point updates. It provides comparable performance and is
significantly faster than convex optimization techniques used in sparse
processing. We propose a signal model which accounts for dictionary mismatch
and the presence of errors in the weight vector at low signal-to-noise ratios.
A fixed point update equation is derived which incorporates the statistics of
mismatch and weight errors. We also process observations from multiple
dictionaries. Noise variances are estimated using stochastic maximum
likelihood. The derived update equations are studied quantitatively using
beamforming simulations applied to direction-of-arrival (DoA). Performance of
SBL using single- and multi-frequency observations, and in the presence of
aliasing, is evaluated. SwellEx-96 experimental data demonstrates qualitatively
the advantages of SBL.Comment: 11 pages, 8 figure
Adaptive matching pursuit for off-grid compressed sensing
Compressive sensing (CS) can effectively recover a signal when it is sparse
in some discrete atoms. However, in some applications, signals are sparse in a
continuous parameter space, e.g., frequency space, rather than discrete atoms.
Usually, we divide the continuous parameter into finite discrete grid points
and build a dictionary from these grid points. However, the actual targets may
not exactly lie on the grid points no matter how densely the parameter is
grided, which introduces mismatch between the predefined dictionary and the
actual one. In this article, a novel method, namely adaptive matching pursuit
with constrained total least squares (AMP-CTLS), is proposed to find actual
atoms even if they are not included in the initial dictionary. In AMP-CTLS, the
grid and the dictionary are adaptively updated to better agree with
measurements. The convergence of the algorithm is discussed, and numerical
experiments demonstrate the advantages of AMP-CTLS.Comment: 24 pages. 10 figure
Compressed Sensing for Wireless Communications : Useful Tips and Tricks
As a paradigm to recover the sparse signal from a small set of linear
measurements, compressed sensing (CS) has stimulated a great deal of interest
in recent years. In order to apply the CS techniques to wireless communication
systems, there are a number of things to know and also several issues to be
considered. However, it is not easy to come up with simple and easy answers to
the issues raised while carrying out research on CS. The main purpose of this
paper is to provide essential knowledge and useful tips that wireless
communication researchers need to know when designing CS-based wireless
systems. First, we present an overview of the CS technique, including basic
setup, sparse recovery algorithm, and performance guarantee. Then, we describe
three distinct subproblems of CS, viz., sparse estimation, support
identification, and sparse detection, with various wireless communication
applications. We also address main issues encountered in the design of CS-based
wireless communication systems. These include potentials and limitations of CS
techniques, useful tips that one should be aware of, subtle points that one
should pay attention to, and some prior knowledge to achieve better
performance. Our hope is that this article will be a useful guide for wireless
communication researchers and even non-experts to grasp the gist of CS
techniques
FDD Massive MIMO Channel Estimation with Arbitrary 2D-Array Geometry
This paper addresses the problem of downlink channel estimation in
frequency-division duplexing (FDD) massive multiple-input multiple-output
(MIMO) systems. The existing methods usually exploit hidden sparsity under a
discrete Fourier transform (DFT) basis to estimate the cdownlink channel.
However, there are at least two shortcomings of these DFT-based methods: 1)
they are applicable to uniform linear arrays (ULAs) only, since the DFT basis
requires a special structure of ULAs, and 2) they always suffer from a
performance loss due to the leakage of energy over some DFT bins. To deal with
the above shortcomings, we introduce an off-grid model for downlink channel
sparse representation with arbitrary 2D-array antenna geometry, and propose an
efficient sparse Bayesian learning (SBL) approach for the sparse channel
recovery and off-grid refinement. The main idea of the proposed off-grid method
is to consider the sampled grid points as adjustable parameters. Utilizing an
in-exact block majorization-minimization (MM) algorithm, the grid points are
refined iteratively to minimize the off-grid gap. Finally, we further extend
the solution to uplink-aided channel estimation by exploiting the angular
reciprocity between downlink and uplink channels, which brings enhanced
recovery performance.Comment: 15 pages, 9 figures, IEEE Transactions on Signal Processing, 201
Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization
The mathematical theory of super-resolution developed recently by Cand\`{e}s
and Fernandes-Granda states that a continuous, sparse frequency spectrum can be
recovered with infinite precision via a (convex) atomic norm technique given a
set of uniform time-space samples. This theory was then extended to the cases
of partial/compressive samples and/or multiple measurement vectors via atomic
norm minimization (ANM), known as off-grid/continuous compressed sensing (CCS).
However, a major problem of existing atomic norm methods is that the
frequencies can be recovered only if they are sufficiently separated,
prohibiting commonly known high resolution. In this paper, a novel (nonconvex)
sparse metric is proposed that promotes sparsity to a greater extent than the
atomic norm. Using this metric an optimization problem is formulated and a
locally convergent iterative algorithm is implemented. The algorithm
iteratively carries out ANM with a sound reweighting strategy which enhances
sparsity and resolution, and is termed as reweighted atomic-norm minimization
(RAM). Extensive numerical simulations are carried out to demonstrate the
advantageous performance of RAM with application to direction of arrival (DOA)
estimation.Comment: 12 pages, double column, 5 figures, to appear in IEEE Transactions on
Signal Processin
- …