681 research outputs found
Off-the-Grid Line Spectrum Denoising and Estimation with Multiple Measurement Vectors
Compressed Sensing suggests that the required number of samples for
reconstructing a signal can be greatly reduced if it is sparse in a known
discrete basis, yet many real-world signals are sparse in a continuous
dictionary. One example is the spectrally-sparse signal, which is composed of a
small number of spectral atoms with arbitrary frequencies on the unit interval.
In this paper we study the problem of line spectrum denoising and estimation
with an ensemble of spectrally-sparse signals composed of the same set of
continuous-valued frequencies from their partial and noisy observations. Two
approaches are developed based on atomic norm minimization and structured
covariance estimation, both of which can be solved efficiently via semidefinite
programming. The first approach aims to estimate and denoise the set of signals
from their partial and noisy observations via atomic norm minimization, and
recover the frequencies via examining the dual polynomial of the convex
program. We characterize the optimality condition of the proposed algorithm and
derive the expected convergence rate for denoising, demonstrating the benefit
of including multiple measurement vectors. The second approach aims to recover
the population covariance matrix from the partially observed sample covariance
matrix by motivating its low-rank Toeplitz structure without recovering the
signal ensemble. Performance guarantee is derived with a finite number of
measurement vectors. The frequencies can be recovered via conventional spectrum
estimation methods such as MUSIC from the estimated covariance matrix. Finally,
numerical examples are provided to validate the favorable performance of the
proposed algorithms, with comparisons against several existing approaches.Comment: 14 pages, 10 figure
On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization
The use of multichannel data in line spectral estimation (or frequency
estimation) is common for improving the estimation accuracy in array
processing, structural health monitoring, wireless communications, and more.
Recently proposed atomic norm methods have attracted considerable attention due
to their provable superiority in accuracy, flexibility and robustness compared
with conventional approaches. In this paper, we analyze atomic norm
minimization for multichannel frequency estimation from noiseless compressive
data, showing that the sample size per channel that ensures exact estimation
decreases with the increase of the number of channels under mild conditions. In
particular, given channels, order samples per channel, selected randomly from
equispaced samples, suffice to ensure with high probability exact
estimation of frequencies that are normalized and mutually separated by at
least . Numerical results are provided corroborating our analysis.Comment: 14 pages, double column, to appear in IEEE Trans. Information Theor
Alternating projections gridless covariance-based estimation for DOA
We present a gridless sparse iterative covariance-based estimation method
based on alternating projections for direction-of-arrival (DOA) estimation. The
gridless DOA estimation is formulated in the reconstruction of
Toeplitz-structured low rank matrix, and is solved efficiently with alternating
projections. The method improves resolution by achieving sparsity, deals with
single-snapshot data and coherent arrivals, and, with co-prime arrays,
estimates more DOAs than the number of sensors. We evaluate the proposed method
using simulation results focusing on co-prime arrays.Comment: 5 pages, accepted by (ICASSP 2021) 2021 IEEE International Conference
on Acoustics, Speech, and Signal Processin
Multiple and single snapshot compressive beamforming
For a sound field observed on a sensor array, compressive sensing (CS)
reconstructs the direction-of-arrival (DOA) of multiple sources using a
sparsity constraint. The DOA estimation is posed as an underdetermined problem
by expressing the acoustic pressure at each sensor as a phase-lagged
superposition of source amplitudes at all hypothetical DOAs. Regularizing with
an -norm constraint renders the problem solvable with convex
optimization, and promoting sparsity gives high-resolution DOA maps. Here, the
sparse source distribution is derived using maximum a posteriori (MAP)
estimates for both single and multiple snapshots. CS does not require inversion
of the data covariance matrix and thus works well even for a single snapshot
where it gives higher resolution than conventional beamforming. For multiple
snapshots, CS outperforms conventional high-resolution methods, even with
coherent arrivals and at low signal-to-noise ratio. The superior resolution of
CS is demonstrated with vertical array data from the SWellEx96 experiment for
coherent multi-paths.Comment: In press Journal of Acoustical Society of Americ
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