File Exchange

image thumbnail

Circulant Embedding method for generating stationary Gaussian field

version 2.0.0.0 (2.24 KB) by Zdravko Botev
Fast simulation of Gaussian random fields via the Fast Fourier Transform

6 Downloads

Updated 22 Jan 2016

View License

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

Comments and Ratings (2)

Please help me to understand what does it mean and tell me how to do it-
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

Knight Short

Very helpful code.

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?

Thank you for your consideration.

Best regards.

Updates

2.0.0.0

- rewritten as an m-file
- reference updated

MATLAB Release Compatibility
Created with R2015b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Discover Live Editor

Create scripts with code, output, and formatted text in a single executable document.


Learn About Live Editor