215 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
Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling
Solving linear regression problems based on the total least-squares (TLS)
criterion has well-documented merits in various applications, where
perturbations appear both in the data vector as well as in the regression
matrix. However, existing TLS approaches do not account for sparsity possibly
present in the unknown vector of regression coefficients. On the other hand,
sparsity is the key attribute exploited by modern compressive sampling and
variable selection approaches to linear regression, which include noise in the
data, but do not account for perturbations in the regression matrix. The
present paper fills this gap by formulating and solving TLS optimization
problems under sparsity constraints. Near-optimum and reduced-complexity
suboptimum sparse (S-) TLS algorithms are developed to address the perturbed
compressive sampling (and the related dictionary learning) challenge, when
there is a mismatch between the true and adopted bases over which the unknown
vector is sparse. The novel S-TLS schemes also allow for perturbations in the
regression matrix of the least-absolute selection and shrinkage selection
operator (Lasso), and endow TLS approaches with ability to cope with sparse,
under-determined "errors-in-variables" models. Interesting generalizations can
further exploit prior knowledge on the perturbations to obtain novel weighted
and structured S-TLS solvers. Analysis and simulations demonstrate the
practical impact of S-TLS in calibrating the mismatch effects of contemporary
grid-based approaches to cognitive radio sensing, and robust
direction-of-arrival estimation using antenna arrays.Comment: 30 pages, 10 figures, submitted to IEEE Transactions on Signal
Processin
OMP-type Algorithm with Structured Sparsity Patterns for Multipath Radar Signals
A transmitted, unknown radar signal is observed at the receiver through more
than one path in additive noise. The aim is to recover the waveform of the
intercepted signal and to simultaneously estimate the direction of arrival
(DOA). We propose an approach exploiting the parsimonious time-frequency
representation of the signal by applying a new OMP-type algorithm for
structured sparsity patterns. An important issue is the scalability of the
proposed algorithm since high-dimensional models shall be used for radar
signals. Monte-Carlo simulations for modulated signals illustrate the good
performance of the method even for low signal-to-noise ratios and a gain of 20
dB for the DOA estimation compared to some elementary method
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