I was just reading up on the Gaussian pyramid and the Laplacian pyramid, used in compression applications of image. The source is here - Carnegie Mellon 16-385 Computer Vision - Spring 2019, Lecture 3 - Image Pyramids and Frequency Domain.
The slide claims that during Laplacian Pyramid based compression, the original image can be reconstructed back perfectly, because of saving the residuals images.
My understanding of the process is as follows
Convolve original scale image with a Gaussian
Compute the residual image, and save it
Downsample the convolved image, dropping alternate row and column to get to the next level (lower size image).
- Repeat process at this scale, till you reach lowest resolution desired.
Now, it says that given the lowest size image, and the residuals, we can reconstruct back the highest size image.
However, since we are dropping alternate rows and columns while downsampling, isn't this information lost? How can the reconstruction be perfect?