  In information fusion, one is often confronted with the following problem:
given a preexisting set of measurements about an unknown quantity, what new
measurements should one collect in order to accomplish a given fusion task with
optimal accuracy and efficiency. We illustrate just how difficult this problem
can become by considering one of its more simple forms: when the unknown
quantity is a vector in a Hilbert space, the task itself is vector
reconstruction, and the measurements are linear functionals, that is, inner
products of the unknown vector with given measurement vectors. Such
reconstruction problems are the subject of frame theory. Here, we can measure
the quality of a given frame by the average reconstruction error induced by
noisy measurements; the mean square error is known to be the trace of the
inverse of the frame operator. We discuss preliminary results which help
indicate how to add new vectors to a given frame in order to reduce this mean
square error as much as possible.
