  Gaussian filters have applications in a variety of areas in computer science,
from computer vision to speech recognition. The collapsing sum is a matrix
operator that was recently introduced to study Gaussian filters
combinatorially. In this paper, we view the collapsing sum from a discrete
tomographical perspective and examine the recoverability of its preimages as a
matrix completion problem. Using bipartite graphs, we derive a necessary and
sufficient condition for a partial matrix to be extended to a preimage of a
given matrix.
