ABSTRACT
We have seen that there is an intimate relationship between resolution and the oscillation properties of sums of oscillating functions, whether or not inversion is involved in the problem. In this chapter, we continue to explore this relationship and we look at the resolution level of a solution to a linear inverse problem in terms of the noise level on the data. It is worth reminding the reader that, provided the forward operator for the inverse problem has a trivial null-space, in the absence of noise, there is no theoretical limit to resolution. However, the type of linear inverse problem we are interested in here typically involves the object of interest being multiplied by some smooth kernel, commonly an instrumental response function, and then integrated over the support of the object. The result is then perturbed by noise to form the data. In this case, there is an effective non-trivial null-space, determined by the noise level, and hence there is a limit to achievable resolution.
