Isn't this bad that different part of the images are experiencing aliasing as we downsample or upsample? We would need to be able to combine and fuse together all of the previous samples of images into one image for their to be no blurring in the foreground or aliasing in the background right? Or can we sample different parts the image with different sample rates?
I believe this problem is solved with mipmaps. As is explained later, for each sample we take we also look at how "far away" the neighboring samples in screen space are in texture space, and choose the appropriate level of the mipmap that way.