# Least squares parameter correlation

1. May 5, 2015

### vibe3

I am trying to solve a large least squares inversion (inverting data for the modeled sources), and find that my parameters describing 1 source are highly correlated with the parameters describing the second source.

Can anyone recommend a technique or reference which discusses how to reduce the correlation between parameters in a least squares system? I have already tried Tikhonov regularization (damping each set of parameters) with no luck.

2. May 8, 2015

I used Thikonov in my MSc thesis, and it is a genera method used on ill - posed problems, and it works fine. What you usually find is some correlation between a set of data (the one you one to calculate) with some "noise" of this data. Thikonov used the parameter $$\alpha$$ to regularize the solution. You may calculate the residual norm (RN) between your desired data and the one you obtain. However, using Thikonov regularization means to include this regulator $$\alpha |S|^{2}$$ in the residual norm and minimize it, where S is the solution. The problem with this method is a non- well stablished criterion to find the appropiate value of the parameter.

I suggest you to take a look at the L curves and S curves an its definitions,I hope I gave you a taste about it.