PCA Feature extraction for quantitative prediction

Hi. What kind of images are these? Are these natural images? Most computer vision problems use hand designed features like SIFT or HOG. Do you think these might be helpful for your task? What is the resolution of your images? Usually it's not feasible to do a PCA on whole images. Also it would assume that all images have the same size. Is that true for your application? If you want to extract features, I would rather try to do this on a patch level. Can you say anything about the number you try to predict?

They are standardized computer generated images of a geometric shape. The parameter is a measure of its geometry. It's not directly possible to measure the geometry since there is a large amount of noise. One could use image processing techniques to reduce the noise, but there still would be a large error associated with the calculations.

Those techniques you mentioned sound interesting. Are they used in conjunction with ML algorithms to create a feature vector for regression?

I am not quite sure I understand the question. They are usually used as the input for classification but of course they could also be used as input to regression. One could for example use SVR on these features.

Noise reduction techniques can remove gaussian noise and many other forms of noise with extreme ease. you should give them a go. Think of it this way (90% accurate, 10% fiction): anything that can find this underlying parameter reliably is implicitly denoising your image, or cutting through the noise to remaining relevant parameters.