Artículos

Sampling – Reconstruction Procedure of Gaussian Fields

Procedimiento para el Muestreo y Reconstrucción de Campos Gausianos

Vladimir Kazakov¹ and Sviatoslav Afrikanov²

1 Dept. of Telecommunications, the Superior School of Mechanical and Electrical Engineering of the National
Polytechnical Institute of Mexico. Unidad Zacatenco,
C. P. 07738, D.F.; Mexico. Tel: (5255) 5729–60–00, ext. 54757.
vkazakov41@hotmail.com

2 The Corporation "Fazotron–NIR", Moscow, Russia.
africanov@mail.ru

Article received on June 04, 2004; accepted on August 11, 2005

Abstract

The description of the optimal Sampling – Reconstruction Procedure (SRP) of Gaussian fields is given on the basis of the conditional mean rule when the quantity of samples is limited. The Gaussian fields are described by two types of space covariance function: exponential and Gaussian. A lot of both reconstruction and reconstruction error surfaces are obtained by numerical calculation. We changed the type of the covariance functions; the type of sampling (uniform: triangular, square, etc. and non – uniform: polar, spiral, and arbitrary); the quantity of the samples; the distances between the samples; and radii of the covariance functions of both axes. We demonstrate how all above mentioned factors influence on principal optimal SRP characteristics. The results of the calculations have clear interpretations.

Keywords: Gaussian Fields, Uniform and Non – Uniform Sampling, Reconstruction Functions, Reconstruction Error Functions.

Resumen

La descripción del Procedimiento óptimo de Muestreo – Reconstrucción de los procesos Gaussianos esta dada en base a la regla de la media condicional cuando la cantidad de las muestras es limitada. Los Campos Gaussianos están descritos por dos diferentes funciones espaciales de covarianza: exponencial y Gaussiana. Varias superficies de reconstrucción y de error de reconstrucción son obtenidas a partir de los cálculos numéricos. Cambiamos el tipo de las funciones de covarianza; el modo de muestreo (uniforme: triangular, cuadrada, etc. y no uniforme: polar, espiral y arbitraria); la cantidad de muestras; la distancia entre las muestras; el radio de las funciones de covarianza en ambos ejes. Demostramos como estos factores influyen en las principales características del Procedimiento óptimo de Muestreo – Reconstrucción.

Palabras claves: Campos Gaussianos, Muestreo Uniforme y no Uniforme, Funciones de Reconstrucción, Funciones de Error de Reconstrucción.
2000 Mathematics subjects classification –60Hxx, 94A20

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Acknowledgement

This work has been partially supported by Consejo Nacional de Ciencia y Tecnologia (CONACYT) of Mexico under Project No 31472 and by National Polytecnical Institute of Mexico (IPN) under Project No 990350.

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