Paper Info
Title
Multidimensional factorization through helical mapping.
Abstract
This paper proposes a new perspective on the problem of multidimensional spectral factorization, through helical mapping: d-dimensional (dD) data arrays are vectorized, processed by 1D cepstral analysis and then remapped onto the original space. Partial differential equations (PDEs) are the basic framework to describe the evolution of physical phenomena. We observe that the minimum phase helical solution asymptotically converges to the dD semi-causal solution, and allows us to decouple the two solutions arising from PDEs describing physical systems. We prove this equivalence in the theoretical framework of cepstral analysis, and we also illustrate the validity of helical factorization through a 2D wave propagation example and a 3D application to helioseismology. HighlightsWe apply helical mapping (or vectorization) to ND spectral factorization.Effects of the helical map are proved in the cepstral and Z-Transform domain.The helical solution asymptotically converges to the ND solution.Helical map can cancel the back propagating solution of the wave equation.We apply our results to simulated data and to real solar data for helioseismology.
Year
DOI
Venue
2017
10.1016/j.sigpro.2016.08.014
Signal Processing
Keywords
DocType
Volume
Multidimensional filtering,Cepstral analysis,Spectral factorization,Blind deconvolution,Minimum phase,Causality
Journal
abs/1603.02558
Issue
ISSN
Citations 
C
0165-1684
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Francesca Raimondi151.49
Pierre Comon23856716.85
Olivier J. j. Michel323223.78
Umberto Spagnolini491691.86