Fields of nonlinear regression models for inversion of satellite data

Details Fields of nonlinear regression models for inversion of satellite data Fields of nonlinear regression models for inversion of satellite data

Aug 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004georl..3116304p&link_type=abstract

Geophysical Research Letters, Volume 31, Issue 16, CiteID L16304

Physics

Optics

Mathematical Geophysics: Inverse Theory, Oceanography: General: Remote Sensing And Electromagnetic Processes (0689), Mathematical Geophysics: Modeling, Oceanography: Biological And Chemical: Optics, Oceanography: Biological And Chemical: Plankton

Scientific paper

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.

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