938 research outputs found
A Compact Formulation for the Mixed-Norm Minimization Problem
Parameter estimation from multiple measurement vectors (MMVs) is a
fundamental problem in many signal processing applications, e.g., spectral
analysis and direction-of- arrival estimation. Recently, this problem has been
address using prior information in form of a jointly sparse signal structure. A
prominent approach for exploiting joint sparsity considers mixed-norm
minimization in which, however, the problem size grows with the number of
measurements and the desired resolution, respectively. In this work we derive
an equivalent, compact reformulation of the mixed-norm
minimization problem which provides new insights on the relation between
different existing approaches for jointly sparse signal reconstruction. The
reformulation builds upon a compact parameterization, which models the
row-norms of the sparse signal representation as parameters of interest,
resulting in a significant reduction of the MMV problem size. Given the sparse
vector of row-norms, the jointly sparse signal can be computed from the MMVs in
closed form. For the special case of uniform linear sampling, we present an
extension of the compact formulation for gridless parameter estimation by means
of semidefinite programming. Furthermore, we derive in this case from our
compact problem formulation the exact equivalence between the
mixed-norm minimization and the atomic-norm minimization. Additionally, for the
case of irregular sampling or a large number of samples, we present a low
complexity, grid-based implementation based on the coordinate descent method
Unsupervised Parameter Estimation using Model-based Decoder
In this work, we consider the use of a model-based decoder in combination
with an unsupervised learning strategy for direction-of-arrival (DoA)
estimation. Relying only on unlabeled training data we show in our analysis
that we can outperform existing unsupervised machine learning methods and
classical methods. The proposed approach consists of introducing a model-based
decoder in an autoencoder architecture which leads to a meaningful
representation of the statistical model in the latent space of the autoencoder.
Our numerical simulations show that the performance of the presented approach
is not affected by correlated signals and performs well for both, uncorrelated
and correlated, scenarios. This is a result of the fact, that, in the proposed
framework, the signal covariance matrix and the DOAs are estimated
simultaneously.Comment: Submitted to IEEE for possible publicatio
Variational Bayesian Inference of Line Spectra
In this paper, we address the fundamental problem of line spectral estimation
in a Bayesian framework. We target model order and parameter estimation via
variational inference in a probabilistic model in which the frequencies are
continuous-valued, i.e., not restricted to a grid; and the coefficients are
governed by a Bernoulli-Gaussian prior model turning model order selection into
binary sequence detection. Unlike earlier works which retain only point
estimates of the frequencies, we undertake a more complete Bayesian treatment
by estimating the posterior probability density functions (pdfs) of the
frequencies and computing expectations over them. Thus, we additionally capture
and operate with the uncertainty of the frequency estimates. Aiming to maximize
the model evidence, variational optimization provides analytic approximations
of the posterior pdfs and also gives estimates of the additional parameters. We
propose an accurate representation of the pdfs of the frequencies by mixtures
of von Mises pdfs, which yields closed-form expectations. We define the
algorithm VALSE in which the estimates of the pdfs and parameters are
iteratively updated. VALSE is a gridless, convergent method, does not require
parameter tuning, can easily include prior knowledge about the frequencies and
provides approximate posterior pdfs based on which the uncertainty in line
spectral estimation can be quantified. Simulation results show that accounting
for the uncertainty of frequency estimates, rather than computing just point
estimates, significantly improves the performance. The performance of VALSE is
superior to that of state-of-the-art methods and closely approaches the
Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on
Signal Processin
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