_a priori_ in NNLS optimization

Hello everyone,

I'm currently trying to use the lsqnonneg function (NNLS) for my optimization, WITH regularization (rNNLS). For my problem, here's the scheme :

• 1) compute NNLS, without regulrization : I pick the RMSE(NNLS) and store it.
• 2) compute rNNLS, with a regularization factor \lambda : \lambda is chosen so that RMSE(rNNLS)=1,02*RMSE(NNLS).
• 3) compute a priori using the results of the rNNLS optimization, whatever the method is, it's correct according to the litterature
• 4) compute a new regularized NNLS - let's call it aprNNLS for rNNLS with a priori, but here's the limitation : how do I choose my regularization factor \lambda ?

The same litterature as 3) advise to act similarly as in the step 2), i.e. choosing \lambda so that RMSE(aprNNLS)=1,02*RMSE(NNLS), but RMSE(aprNNLS) is almost always 10 times superior RMSE(NNLS), even if the fitting is really similar to the rNNLS method ...!

So, fundamentally, either this automated method isn't adapted, or I missed some information about the using of a priori in the NNLS algorithm.

What's your opinion ?

-Lucas