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Fields of nonlinear regression models for inversion of satellite data
Author(s) -
Pelletier Bruno,
Frouin Robert
Publication year - 2004
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2004gl019840
Subject(s) - multilinear map , inversion (geology) , nonlinear system , mathematics , ridge , interpolation (computer graphics) , computer science , geology , physics , pure mathematics , artificial intelligence , motion (physics) , paleontology , structural basin , quantum mechanics
A solution is provided to a common inverse problem in satellite remote sensing, the retrieval of a variable y from a vector x of explanatory variables influenced by a vector t of conditioning variables. The solution is in the general form of a field of nonlinear regression models, i.e., the relation between y and x is modeled as a map from some space to a subset of a function space. Elementary yet important mathematical results are presented for fields of shifted ridge functions, selected for their approximation properties. These fields are shown to span a dense set and to inherit the approximation properties of shifted ridge functions. A serious mathematical difficulty regarding the practical construction of continuous fields of shifted ridge functions is pointed out; it is circumvented while providing grounding to a large class of construction methodologies. Within this class, a construction scheme that builds upon multilinear interpolation is described. When applied to the retrieval of upper‐ocean chlorophyll‐a concentration from space, the solution shows potential for improved accuracy compared with existing algorithms.