Line Spectrum Estimation Research Articles

New Method of Sparse Parameter Estimation in Separable Models and Its Use for Spectral Analysis of Irregularly Sampled Data

Separable models occur frequently in spectral analysis, array processing, radar imaging and astronomy applications. Statistical inference methods for these models can be categorized in three large classes: parametric, nonparametric (also called “dense”) and semiparametric (also called “sparse”). We begin by discussing the advantages and disadvantages of each class. Then we go on to introduce a new semiparametric/sparse method called SPICE (a semiparametric/sparse iterative covariance-based estimation method). SPICE is computationally quite efficient, enjoys global convergence properties, can be readily used in the case of replicated measurements and, unlike most other sparse estimation methods, does not require any subtle choices of user parameters. We illustrate the statistical performance of SPICE by means of a line-spectrum estimation study for irregularly sampled data.

New methods for fitting multiple sinusoids from irregularly sampled data

A novel framework is proposed for the estimation of multiple sinusoids from irregularly sampled time series. This spectral analysis problem is addressed as an under-determined inverse problem, where the spectrum is discretized on an arbitrarily thin frequency grid. As we focus on line spectra estimation, the solution must be sparse, i.e. the amplitude of the spectrum must be zero almost everywhere. Such prior information is taken into account within the Bayesian framework. Two models are used to account for the prior sparseness of the solution, namely a Laplace prior and a Bernoulli–Gaussian prior, associated to optimization and stochastic sampling algorithms, respectively. Such approaches are efficient alternatives to usual sequential prewhitening methods, especially in case of strong sampling aliases perturbating the Fourier spectrum. Both methods should be intensively tested on real data sets by physicists.

Two-dimensional line spectrum estimation by polar coordinate ar models

In this paper, a spectrum estimation method is proposed which is based on a two-dimensional autoregressive (AR) model with polar coordinate coefficient arrangement. When the signal is given in terms of an orthogonal coordinate system, such a coordinate system is naturally used for linear prediction in a conventional AR estimation method. The support of the estimation coefficients and the peak shape of the corresponding estimation spectrum are known to be related by a certain rule. By using an AR model in which the coordinate arrangement of the linear prediction is in a polar coordinate, the rotation of the coordinate region keeps an AR model in the same polar coordinate form. Hence, it is possible to determine the relative positional relationship between the estimated spectrum shape and the coefficient mask. It is shown that the present method can estimate the spectrum with a high resolution by using this relationship and avoiding the interference between the spectral peaks.