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### Highlights from Circulant Embedding method for generating stationary Gaussian field

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# Circulant Embedding method for generating stationary Gaussian field

### Zdravko Botev (view profile)

02 Nov 2012 (Updated )

Fast simulation of Gaussian random fields via the Fast Fourier Transform

File Information
Description

simulating stationary Gaussian field over an 'm' times 'n' grid
INPUT:
- 'm' and 'n' for evaluating the field over the m*n grid;
note that size of covariance matrix is m^2*n^2;
- scalar function rho(h), where 'h' is a two dimensional vector
input and cov(X_t,Y_s)=rho(t-s) is the cov. function of a
2-dimensional stationary Gaussian field; see reference below;
OUTPUT:
- two statistically independent fields 'field1' and 'field2'
over the m*n grid;
- vectors 'tx' and 'ty' so that the field is plotted via
imagesc(tx,ty,field1)
Example:
rho=@(h)((1-h(1)^2/50^2-h(1)*h(2)/(15*50)-h(2)^2/15^2)...
*exp(-(h(1)^2/50^2+h(2)^2/15^2))); % define covariance function
stationary_Gaussian_process(512,384,rho); % plot when no output wanted
Reference:
Kroese, D. P., & Botev, Z. I. (2015). Spatial Process Simulation.
In Stochastic Geometry, Spatial Statistics and Random Fields(pp. 369-404)
Springer International Publishing, DOI: 10.1007/978-3-319-10064-7_12

Acknowledgements

This file inspired Fractional Brownian Field Or Surface Generator.

Required Products MATLAB
MATLAB release MATLAB 8.6 (R2015b)
MATLAB Search Path
`/`
01 Mar 2016 ARVINDER KAUR

### ARVINDER KAUR (view profile)

Realistic spatially correlated speckle noise in ultrasound images can be simulated by low-pass filtering a complex Gaussian random field and taking the magnitude of filtered output.The speckle noise with different covariance functions are introduced under different noise cases.These are-Matern covariance function,Spherical covariance function,Exponential covariance function and Rational quadratic covariance function.
Mean of Gaussian random field=0

Comment only
06 Jun 2014 Knight Short

### Knight Short (view profile)

I am interested in How to use this circulant embedding method to generate a 3 dimensional stationary processes. The book does not describe that case in detail. Could we have a further communication?