123helloworld123 / a2pk

Generate stocastic Gaussian realization constrained to a coarse scale image.

A2PK

This MATLAS package allows you to generate stocastic Gaussin simulation at a fine-scale based on a coarse scale image of the same domain. This is done through area-to-point kriging, a co-kriging estimation where the coase-scale is view as a secondary variable which allows the construction of the cross-covariance easily.

Area-to-point kriging live-script

The scripts below are generated with Matlab live-script and allow your to see step by step what is A2PK and how to use it.

• A2PK Gaussian Live Script is the easiest place to start as this guide you through the computation of the simulation
• A2PK Conditional Gaussian expend the previous Live Script with the conditional case
• A2PK.m is the matlab function file which can be used for any application.

Application to Eletrical Resistivity Tomography (ERT)

We applied A2PK to the simulation of a fine-scale scale electrical conductivity field based on the smooth result of an inversion based on ERT. Refers to the ERT folder for all the codes, and more precisely to the publish script script_ERT.mlx.

This work has lead to a paper which is currently under revision. Contact me if you would like a pdf of the draft.

Application to Hydraulic tomography (HT)

Refers to the HT folder, and more precisely to the script used to generate the dataset and the result. I'll try to make an html page of this code soon. This is an ongoing research.

Reference

Some useful readings

• Kyriakidis, Phaedon C. 2004. “A Geostatistical Framework for Area-to-Point Spatial Interpolation.” Geographical Analysis 36(3):259–89. Retrieved (http://doi.wiley.com/10.1353/geo.2004.0009).
• Yoo, E. H. and Phaedon C. Kyriakidis. 2006. “Area-to-Point Kriging with Inequality-Type Data.” Journal of Geographical Systems 8(4):357–90.
• Yoo, Eun Hye and P. C. Kyriakidis. 2008. “Area-to-Point Prediction Under Boundary Conditions.” Geographical Analysis 40(4):355–79. Retrieved (http://doi.wiley.com/10.1111/j.0016-7363.2008.00734.x).
• Yoo, E. H. and P. C. Kyriakidis. 2009. “Area-to-Point Kriging in Spatial Hedonic Pricing Models.” Journal of Geographical Systems 11(4):381–406.
• Atkinson, Peter M. 2013. “Downscaling in Remote Sensing.” International Journal of Applied Earth Observation and Geoinformation 22(1):106–14. Retrieved (http://dx.doi.org/10.1016/j.jag.2012.04.012).
• Atkinson, Peter M., Eulogio Pardo-Igúzquiza, and Mario Chica-Olmo. 2008. “Downscaling Cokriging for Super-Resolution Mapping of Continua in Remotely Sensed Images.” IEEE Transactions on Geoscience and Remote Sensing 46(2):573–80.
• Liu, X. H., P. C. Kyriakidis, and M. F. Goodchild. 2008. “Population‐density Estimation Using Regression and Area‐to‐point Residual Kriging.” International Journal of Geographical Information Science 22(4):431–47. Retrieved (http://www.tandfonline.com/doi/abs/10.1080/13658810701492225).
• Gotway, Carol A. and Linda J. Young. 2002. “Combining Incompatible Spatial Data.” Journal of the American Statistical Association 97(458):632–48. Retrieved (http://www.tandfonline.com/doi/abs/10.1198/016214502760047140). Kyriakidis, Phaedon C. and Eun Hye Yoo. 2005. “Geostatistical Prediction and Simulation of Point Values from Areal Data.” Geographical Analysis 37(2):124–51.