10,938 research outputs found
Bayesian separation of spectral sources under non-negativity and full additivity constraints
This paper addresses the problem of separating spectral sources which are
linearly mixed with unknown proportions. The main difficulty of the problem is
to ensure the full additivity (sum-to-one) of the mixing coefficients and
non-negativity of sources and mixing coefficients. A Bayesian estimation
approach based on Gamma priors was recently proposed to handle the
non-negativity constraints in a linear mixture model. However, incorporating
the full additivity constraint requires further developments. This paper
studies a new hierarchical Bayesian model appropriate to the non-negativity and
sum-to-one constraints associated to the regressors and regression coefficients
of linear mixtures. The estimation of the unknown parameters of this model is
performed using samples generated using an appropriate Gibbs sampler. The
performance of the proposed algorithm is evaluated through simulation results
conducted on synthetic mixture models. The proposed approach is also applied to
the processing of multicomponent chemical mixtures resulting from Raman
spectroscopy.Comment: v4: minor grammatical changes; Signal Processing, 200
Joint-Polarization Phase-Noise Estimation and Symbol Detection for Optical Coherent Receivers
The problem of optimal symbol detection in the presence of laser phase noise is studied, for uncoded polarization-multiplexed fiber-optic transmission. To this end, the maximum a posteriori (MAP) symbol detector is presented. Specifically, it is emphasized that obtaining phase-noise point estimates, and treating them as the true values of the phase noise, is in general suboptimal. Furthermore, a pilot-based algorithm that approximates the MAP symbol detector is developed, using approaches adopted from the wireless literature. The algorithm performs joint-polarization phase-noise estimation and symbol detection, for arbitrary modulation formats. Through Monte Carlo simulations, the algorithm is compared to existing solutions from the optical communications literature. It is demonstrated that joint-polarization processing can significantly improve upon the single-polarization case, with respect to linewidth tolerance. Finally, it is shown that with less than 3% pilot overhead, the algorithm can be used with lasers having up to 6 times larger linewidths than the most well-performing blind algorithms can tolerate
Blind channel equalization using weighted subspace methods
This paper addresses the problems of blind channel estimation and symbol detection with second order statistics methods from the received data. It can be shown that this problem is similar to direction of arrival (DOA) estimation, where many solutions like the MUSIC algorithm orPeer ReviewedPostprint (published version
Two-Way Training for Discriminatory Channel Estimation in Wireless MIMO Systems
This work examines the use of two-way training to efficiently discriminate
the channel estimation performances at a legitimate receiver (LR) and an
unauthorized receiver (UR) in a multiple-input multiple-output (MIMO) wireless
system. This work improves upon the original discriminatory channel estimation
(DCE) scheme proposed by Chang et al where multiple stages of feedback and
retraining were used. While most studies on physical layer secrecy are under
the information-theoretic framework and focus directly on the data transmission
phase, studies on DCE focus on the training phase and aim to provide a
practical signal processing technique to discriminate between the channel
estimation performances at LR and UR. A key feature of DCE designs is the
insertion of artificial noise (AN) in the training signal to degrade the
channel estimation performance at UR. To do so, AN must be placed in a
carefully chosen subspace based on the transmitter's knowledge of LR's channel
in order to minimize its effect on LR. In this paper, we adopt the idea of
two-way training that allows both the transmitter and LR to send training
signals to facilitate channel estimation at both ends. Both reciprocal and
non-reciprocal channels are considered and a two-way DCE scheme is proposed for
each scenario. {For mathematical tractability, we assume that all terminals
employ the linear minimum mean square error criterion for channel estimation.
Based on the mean square error (MSE) of the channel estimates at all
terminals,} we formulate and solve an optimization problem where the optimal
power allocation between the training signal and AN is found by minimizing the
MSE of LR's channel estimate subject to a constraint on the MSE achievable at
UR. Numerical results show that the proposed DCE schemes can effectively
discriminate between the channel estimation and hence the data detection
performances at LR and UR.Comment: 1
Multisource Self-calibration for Sensor Arrays
Calibration of a sensor array is more involved if the antennas have direction
dependent gains and multiple calibrator sources are simultaneously present. We
study this case for a sensor array with arbitrary geometry but identical
elements, i.e. elements with the same direction dependent gain pattern. A
weighted alternating least squares (WALS) algorithm is derived that iteratively
solves for the direction independent complex gains of the array elements, their
noise powers and their gains in the direction of the calibrator sources. An
extension of the problem is the case where the apparent calibrator source
locations are unknown, e.g., due to refractive propagation paths. For this
case, the WALS method is supplemented with weighted subspace fitting (WSF)
direction finding techniques. Using Monte Carlo simulations we demonstrate that
both methods are asymptotically statistically efficient and converge within two
iterations even in cases of low SNR.Comment: 11 pages, 8 figure
Maximum-a-posteriori estimation with Bayesian confidence regions
Solutions to inverse problems that are ill-conditioned or ill-posed may have
significant intrinsic uncertainty. Unfortunately, analysing and quantifying
this uncertainty is very challenging, particularly in high-dimensional
problems. As a result, while most modern mathematical imaging methods produce
impressive point estimation results, they are generally unable to quantify the
uncertainty in the solutions delivered. This paper presents a new general
methodology for approximating Bayesian high-posterior-density credibility
regions in inverse problems that are convex and potentially very
high-dimensional. The approximations are derived by using recent concentration
of measure results related to information theory for log-concave random
vectors. A remarkable property of the approximations is that they can be
computed very efficiently, even in large-scale problems, by using standard
convex optimisation techniques. In particular, they are available as a
by-product in problems solved by maximum-a-posteriori estimation. The
approximations also have favourable theoretical properties, namely they
outer-bound the true high-posterior-density credibility regions, and they are
stable with respect to model dimension. The proposed methodology is illustrated
on two high-dimensional imaging inverse problems related to tomographic
reconstruction and sparse deconvolution, where the approximations are used to
perform Bayesian hypothesis tests and explore the uncertainty about the
solutions, and where proximal Markov chain Monte Carlo algorithms are used as
benchmark to compute exact credible regions and measure the approximation
error
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
Fir system identification using a linear combination of cumulants
A general linear approach to identifying the parameters of a moving average (MA) model from the statistics of the output is developed. It is shown that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. This result is then used to obtain a new well-conditioned linear method to estimate the MA parameters of a nonGaussian process. The proposed approach does not require a previous estimation of the filter order. Simulation results show improvement in performance with respect to existing methods.Peer ReviewedPostprint (published version
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
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