Generate new image from principal components of many images

[christmasfuture]

1. Homework Statement

I'm having a bit of difficulty with a neuroscience course - it's about the primary visual cortex.

I have a bunch of image patches (16*16) and I need to generate synthesised images using principal component analysis as a generative model. I reshaped the images to vectors with 256 elements (50000 observations) and got the principal components (a 256*256 matrix)

Now I need to 'generate synthesized images using my PCA as a generative model and assuming that the marginal distribution of the components is Gaussian with a variance equal to the variance of the learned component.'

I've thought about it for ages, and I just can't understand what the assignment is trying to get me to do. Could anyone please please please offer me some help? I'm really stuck.

2. Homework Equations

3. The Attempt at a Solution

I thougth perhaps a new image would be x1p1 + x2p2 + x3p3... etc where pi is a principal component and x is a gaussian distribution of coefficients, but that doesn't seem right.

 

[nilesh_pat]

I think the assignment is asking you to generate a synthesised image by taking a sample from a Gaussian distribution with a variance equal to the variance of the principal components, and then multiplying it by the principal components. This should give you an image that is generated by the model based on the data you have provided.