Toeplitz matrix with an image

I'm struggling to understand something. So far I understood this : x is 3x3 matrix and W is a 2x2 matrix

a) extend W to be a 4X9 matrix and flatten x to be 9x1

b) multiply the Toeplitz matrix and the vector

the part that I don't understand is how can do the same thing with an 400 * 400 image grayscaled before and 3x3 filter.

x = 400 * 400

w = 3 * 3

h = 9 * 160 000

x_flatten = 160 000

output = x_flatten * h ??

I can't figure it out how can I play with the shape to achieve the same principles to be able to retrieve my image after

thank you

Toeplitz matrix is used to get the result of the convolution between two matices. Suppose X is of shape (n,n) and W is of shape (m,m). Then your Toeplitz matrix h will be of shape ((n-m+1)^2 , n^2) and your flatten matrix X_flatten will become (n^2, 1). Then the resulting multiplication will produce vector of the length (n-m+1)^2, which is exact number of elements of inner convolution. You just need to reshape it back to square.