15,617 research outputs found
Efficient and Accurate Frequency Estimation of Multiple Superimposed Exponentials in Noise
The estimation of the frequencies of multiple superimposed exponentials in
noise is an important research problem due to its various applications from
engineering to chemistry. In this paper, we propose an efficient and accurate
algorithm that estimates the frequency of each component iteratively and
consecutively by combining an estimator with a leakage subtraction scheme.
During the iterative process, the proposed method gradually reduces estimation
error and improves the frequency estimation accuracy. We give theoretical
analysis where we derive the theoretical bias and variance of the frequency
estimates and discuss the convergence behaviour of the estimator. We show that
the algorithm converges to the asymptotic fixed point where the estimation is
asymptotically unbiased and the variance is just slightly above the Cramer-Rao
lower bound. We then verify the theoretical results and estimation performance
using extensive simulation. The simulation results show that the proposed
algorithm is capable of obtaining more accurate estimates than state-of-art
methods with only a few iterations.Comment: 10 pages, 10 figure
Supervised nonlinear spectral unmixing using a post-nonlinear mixing model for hyperspectral imagery
This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data
Parametric high resolution techniques for radio astronomical imaging
The increased sensitivity of future radio telescopes will result in
requirements for higher dynamic range within the image as well as better
resolution and immunity to interference. In this paper we propose a new matrix
formulation of the imaging equation in the cases of non co-planar arrays and
polarimetric measurements. Then we improve our parametric imaging techniques in
terms of resolution and estimation accuracy. This is done by enhancing both the
MVDR parametric imaging, introducing alternative dirty images and by
introducing better power estimates based on least squares, with positive
semi-definite constraints. We also discuss the use of robust Capon beamforming
and semi-definite programming for solving the self-calibration problem.
Additionally we provide statistical analysis of the bias of the MVDR beamformer
for the case of moving array, which serves as a first step in analyzing
iterative approaches such as CLEAN and the techniques proposed in this paper.
Finally we demonstrate a full deconvolution process based on the parametric
imaging techniques and show its improved resolution and sensitivity compared to
the CLEAN method.Comment: To appear in IEEE Journal of Selected Topics in Signal Processing,
Special issue on Signal Processing for Astronomy and space research. 30 page
Group Iterative Spectrum Thresholding for Super-Resolution Sparse Spectral Selection
Recently, sparsity-based algorithms are proposed for super-resolution
spectrum estimation. However, to achieve adequately high resolution in
real-world signal analysis, the dictionary atoms have to be close to each other
in frequency, thereby resulting in a coherent design. The popular convex
compressed sensing methods break down in presence of high coherence and large
noise. We propose a new regularization approach to handle model collinearity
and obtain parsimonious frequency selection simultaneously. It takes advantage
of the pairing structure of sine and cosine atoms in the frequency dictionary.
A probabilistic spectrum screening is also developed for fast computation in
high dimensions. A data-resampling version of high-dimensional Bayesian
Information Criterion is used to determine the regularization parameters.
Experiments show the efficacy and efficiency of the proposed algorithms in
challenging situations with small sample size, high frequency resolution, and
low signal-to-noise ratio
Atmospheric tomography with separate minimum variance laser and natural guide star mode control
This paper introduces a novel, computationally efficient, and practical atmospheric tomography wavefront control architecture with separate minimum variance laser and natural guide star mode estimation. The architecture is applicable to all laser tomography systems, including multi conjugate adaptive optics (MCAO), laser tomography adaptive optics (LTAO), and multi object adaptive optics (MOAO) systems. Monte Carlo simulation results for the Thirty Meter Telescope (TMT) MCAO system demonstrate its benefit over a previously introduced “ad hoc” split MCAO architecture, calling for further in-depth analysis and simulations over a representative ensemble of natural guide star (NGS) asterisms with optimized loop frame rates and modal gains
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