Is It Possible to Reconstruct the Original Image from Laplacian Pyramid? In our computer vision course, my professor said we can reconstruct the original image from the Laplacian pyramid. It just feels to me that information is lost after doing subsampling and upsampling. 

Is it possible? If so, why? Are the reconstructed image exactly the same as the original pixel by pixel? And is this answer correct?

Generate Laplacian pyramid $(f_2, h_1, h_0)$ from image $f_0$:



Reconstruct $f_0$ from Laplacian pyramid:



source
This depends on the order of upsampling and downsampling.
If the order is correct, then you won't throw away anything and thus you should in principle be able to reconstruct the image.

In general:

$$ \left(\uparrow_n\downarrow_n f\right) \neq \left(\downarrow_n\uparrow_n f\right) $$

Similar things are used when using the Wavelet decomposition on a signal, which again uses up- and downsampling combined with the Wavelet filters.