I’ve updated my automatic 2d Gaussian surface fitting function, available in Matlab Central, to add a function to fit Gabors to noisy data. As I’ve discussed previously, fitting a parametric surface to noisy data is pretty trivial whether it’s a Gabor, Gaussian, or otherwise — it’s a straightforward application of numerical optimization that can be done straightforwardly with `lsqcurvefit`

. The annoying bit is choosing the initial parameters when the error surface is non-convex, especially when you have a bunch of data to fit.

The Gaussian surface fitting function does this by an exhaustive search through parameter space, which is made efficient via FFT-based convolution. The new Gabor fitting function uses the fact that the absolute value of the Fourier transform of a Gabor is a Gaussian. It gets a good guess of the orientation, spatial frequency and bandwidth of the Gabor using this fact, locates the approximate position of this Gabor, and then fills in the details with `lsqcurvefit`

.

I’ve removed the function for Gibbs sampling the Gaussian fit; it didn’t work too well in practice with data that does not conform well to the model assumptions. I think this is partially because the posterior is often composed of islands of high-probability separated by a sea of low probability, and the slice sampler is not well adapted to this configuration.

Update: I’ve now added in a Metropolis-Hastings sampling to replace to original Gibbs method. Not sure how much more reliable with will be but this scheme is at least less messy to implement. Let me know.

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