In Gaussian pyramids, the image at each level $I_k$ is constructed by blurring the image at

the previous level $I_{k-1}$ and downsampling it by a factor of $2.$ A Laplacian pyramid, on the

other hand, consists of the difference between the image at each level $(I_k)$ and the upsampled

version of the image in the next level of the Gaussian pyramid $(I_{k+1}).$

Given an image of size $2^n{2}^n$ denoted by $I_0,$ and its Laplacian pyramid representation

denoted by $L_0,$dots,$L_{n-1},$ show how we can reconstruct the original image, using the minimum

information from the Gaussian pyramid. Specify the minimum information required from

the Gaussian pyramid and a closed$-$form expression for reconstructing $I_0.$

Hint: The reconstruction follows a recursive process; What is the base case that contains

the minimum information?