Throughout this course we have created a chain of approximations. Using Monte Carlo we can get a ``exact'' solution at any point. The first approximation was to discretize the environment and project this exact solution onto it. The next level of approximation was to compute our solution within this discretized space by creating a matrix of interactions. Then we introduced an approximate matrix by represinting it hierarchically. Finally, there is computation error that results in inaccurate interactions. Note that we have assumed that the model is exact and that the monitor can display the solution correctly.
Assume the links are exact, and there is extraneous emission on each receiver (either positive or negative) exactly equal to the error. We now have the exact solution (given the structure of the matrix) to the wrong question. We have the wrong initial conditions (emissions). The global effects of this error will be magnified by the propagation throughout the environment, which is due to the norm of the transport operator. This means we need more link accuracy in highly reflective environments than we do in low reflectivity environments.
What we really want is to know the exact effect of the error in an interaction on the rest of the environment. We can't do this exactly, but we can estimate it using the concept of importance.
There are two different reconstruction goals
For a single image, quality is usually the driving factor. Quality can be increased by the following