Multidimensional Variational Line Spectra Estimation
Qi Zhang, Jiang Zhu, Ning Zhang, Zhiwei Xu
2020IEEE Signal Processing Letters15 citationsDOIOpen Access PDF Abstract
The fundamental multidimensional line spectral estimation problem is addressed utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) algorithm, multidimensional VALSE (MDVALSE) is developed. MDVALSE inherits the advantages of VALSE such as automatically estimating the model order, noise variance and providing uncertain degrees of frequency estimates. Compared to VALSE, the multidimensional frequencies of a single component is treated as a whole, and the probability density function (PDF) is projected as independent univariate von Mises distribution to perform tractable inference. Besides, for the initialization, efficient fast Fourier transform (FFT) is adopted to approximate the marginal posterior PDF of frequencies. Numerical results demonstrate the effectiveness of the MDVALSE, compared to state-of-art methods.
Topics & Concepts
MathematicsUnivariateMultidimensional systemsAlgorithmProbability density functionLine (geometry)Applied mathematicsSpectral density estimationEstimation theoryBayesian probabilityMarginal distributionMathematical optimizationvon Mises distributionNoise (video)Fourier transformVariance (accounting)Function (biology)Posterior probabilityDiscrete Fourier transform (general)Stability (learning theory)Distribution (mathematics)Spectral densityComputer scienceFast Fourier transformProbability distributionReal lineTime–frequency analysisMarginal likelihoodPrincipal component analysisMultidimensional signal processingApproximation theoryBayes estimatorLikelihood functionFourier analysisJoint probability distributionStable distributionStatistical modelBayesian linear regressionNoise measurementComponent (thermodynamics)Structural Health Monitoring TechniquesBlind Source Separation TechniquesControl Systems and Identification