I think it was mentioned in class that the only step that JPEG compression loses information is in the quantization stage when we zero out a lot of coefficients. But aren't we also losing information when we are projecting onto a finite discrete basis. These basis vectors only account for a certain range of frequencies correct? What if the image had frequencies that couldn't be represented using the vectors in this basis? (Or is this where the assumption that JPEG doesn't really care about the high frequency changes in images come into play?)
kayvonf
@kapalani. No information is lost when applying the DCT to convert an image's representation from the pixel basis to its representation in the cosine basis (ignoring loss due to issues like numerical precision). The reason is that we are transforming a discretely sampling 8x8 image (we are not projecting a contiguous signal onto the basis). The 8x8 image only captures a finite number of frequencies, so these 64 basis images entirely span the space of 8x8 images.
I think it was mentioned in class that the only step that JPEG compression loses information is in the quantization stage when we zero out a lot of coefficients. But aren't we also losing information when we are projecting onto a finite discrete basis. These basis vectors only account for a certain range of frequencies correct? What if the image had frequencies that couldn't be represented using the vectors in this basis? (Or is this where the assumption that JPEG doesn't really care about the high frequency changes in images come into play?)
@kapalani. No information is lost when applying the DCT to convert an image's representation from the pixel basis to its representation in the cosine basis (ignoring loss due to issues like numerical precision). The reason is that we are transforming a discretely sampling 8x8 image (we are not projecting a contiguous signal onto the basis). The 8x8 image only captures a finite number of frequencies, so these 64 basis images entirely span the space of 8x8 images.