Chapter List

The Two Problems

It is often the case in remote sensing that what we want and what we can measure are related by Fourier transformation. Frequently one of the two functions has bounded support, so that the other one is band-limited. If our measurements are samples of a function of bounded support, we shall say that we are solving a problem of Type One, while if the sampled function is band-limited, we say the problem is of Type Two. As we shall see, these two types of problems are distinct and different techniques are required to solve them.

Throughout this chapter we let F( ?) be defined for ? ? [0 , 2 ?], with

In applications, F( ?) usually represents some physical object of limited extent. In problems of Type Two, remote sensing has provided (usually noisy) values of f( x) for finitely many x.

When algorithms are being developed and tested, one often works with simulations. If the F( ?) to be simulated is specified analytically, we may be able to compute values of f( x) by performing the integrals in Equation (19.1). It may be the case, however, that the integrals cannot be performed exactly or even that F( ?) is represented by a...