We cannot avoid defining ,because without it, any region of zero signal would get an infinite weight. This is likely to lead to undesirable performance: in other words, although with the data of Figure 2 I found rapid convergence to a satisfactory answer, there is no reason that this had to happen. The result could also have failed to converge, or it could have converged to a nonunique answer. This unreliable performance is why academic expositions rarely mention estimating weights from the data, and certainly do not promote the nonlinear-estimation procedure. We have seen here how important these are, however.
I do not want to leave you with the misleading impression that convergence in a simple problem always goes to the desired answer. With the program that made these figures, I could easily have converged to the wrong answer merely by choosing data that contained too much crosstalk. In that case both images would have converged to .Such instability is not surprising, because when exceeds unity, the meanings of and are reversed.