"Laplacian" (DoG) Pyramid
Taking the difference of neighboring levels in the Gaussian pyramid creates a "bandpass filter" at each step in the pyramid.
Such a bandpass filter resembles convolution with a Laplacian kernel, so we take this as an approximation of the Laplacian pyramid.
An image can be reconstructed quite well by collapsing its pyramid. The degree of fidelity will depend upon your method of sampling.
Used a cell array to represent the pyramid.
Used imresize in 'bilinear' mode again, in order to properly invert the downsampling.