Thread Subject: Parameter analysis and reduction with mearurements

Hi all,

I have a problem related to dimensionality reduction / feature selection, but a bit different. Until now, I have not found a working solution. Maybe you can point me into the right direction?

The problem:
Our application requires state-of-the-art image processing for noise reduction. Each new algorithm comes with many parameters. Currently, we can adjust over 200 parameters for noise reduction alone. These parameters need to be tuned by image quality experts. This is very time-consuming, as each time a new algorithm is introduced, the IQ experts need to get familiar with all the parameters.

The solution:
In order to reduce the tuning effort, I would like to automatically analyze and reduce the parameters. So: which parameters are (in-) dependent? Which parameters have a large effect on the IQ and which only small or none? What is the relevant range of all parameters for this application? Is the effect on IQ linear over this range or for example logarithmic?

The measurements
I already mentioned the Image Quality (IQ), but this is a field of research on its own. I intend to use many measurements, such as contrast, noise, sharpness, SSIM, VIF, etc. So where you read IQ, any (combination) of these measures should be read.

The first attempt
Using PCA, simple (and linear!) relations can be found. A simple example: The image processing algorithm used is (Matlab notation):
imOut =(p1+5*p2 )* ( imIm – mean(imIn(:)) ) + mean(imIn(:)) + p3 + p4^2;
I then do 100 iterations with random values for the parameters [p1, p2, p3, p4]. Each iteration the output image is calculated and from that the measurements contrast, brightness and sharpness are calculated.
I now have a parameter matrix of 100x4 and a measurement matrix of 100x3. If I combine these to a 100x7 matrix and run PCA on it, I find relations between p1, p2 and contrast and between p3, p4 and brightness.

The questions
I am looking for approaches where:
- Gives be the kind of relations mentioned under “The solution”
- I can separate the parameter values from the measurement values, as I think they should be dealth with differently for an optimal approach
- Also works for non-linear relations
- Perfect would be an existing Matlab implementation

What kinds of algorithms are available? Can anyone point me into the right direction?