A half-quadratic block-coordinate descent method for spectral estimation
Signal Processing
SAR Image Superresolution via 2-D Adaptive Extrapolation
Multidimensional Systems and Signal Processing
Algorithm 890: Sparco: A Testing Framework for Sparse Reconstruction
ACM Transactions on Mathematical Software (TOMS)
Optimized sinusoid synthesis via inverse truncated fourier transform
IEEE Transactions on Audio, Speech, and Language Processing
Nonlinear regularization techniques for seismic tomography
Journal of Computational Physics
Direction-of-arrival estimation using a mixed l2,0norm approximation
IEEE Transactions on Signal Processing
Estimation of parameters of the weakly damped sinusoidal signals in the frequency domain
Computer Standards & Interfaces
On analysis-based two-step interpolation methods for randomly sampled seismic data
Computers & Geosciences
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We present an iterative nonparametric approach to spectral estimation that is particularly suitable for estimation of line spectra. This approach minimizes a cost function derived from Bayes' theorem. The method is suitable for line spectra since a “long tailed” distribution is used to model the prior distribution of spectral amplitudes. Since the data themselves are used as constraints, phase information can also be recovered and used to extend the data outside the original window. The objective function is formulated in terms of hyperparameters that control the degree of fit and spectral resolution. Noise rejection can also be achieved by truncating the number of iterations. Spectral resolution and extrapolation length are controlled by a single parameter. When this parameter is large compared with the spectral powers, the algorithm leads to zero extrapolation of the data, and the estimated Fourier transform yields the periodogram. When the data are sampled at a constant rate, the algorithm uses one Levinson recursion per iteration. For irregular sampling, the algorithm uses one Cholesky decomposition per iteration. The performance of the algorithm is illustrated with three different problems that arise in geophysical data: (1) harmonic retrieval from a time series contaminated with noise; (2) linear event detection from a finite aperture array of receivers, (3) interpolation/extrapolation of gapped data. The performance of the algorithm as a spectral estimator is tested with the Kay and Marple (1981) data set