ABSTRACT
To help us to understand the problem, I want to introduce the concept of an effective pattern, Q(x) . Suppose we transform the observed data T(xi) by replacing each value with a sum of the form
where the constants mij do not, in fact, depend on i: I shall write just mj in stead of mij. The resulting image is exactly the same as the one I would have gotten if I had
been able to use a different pattern Q(x) instead of P(x).4 It could turn out that, in an attempt to improve the resolution of the image, we inadvertently introduce large side lobes. We might not know that we had done so if we did not plot the effective pattern. In other words, I shall judge the improvement we have attained by comparing P(x) with Q(x) . The advantages of doing this are, first, that I can make the comparison directly, without having to apply it to actual data, and that I can get a good visual impression from plots of P(x) and Q(x) . I first dealt with this problem in Milman (1986); I give a simpler treatment here.
