Simple observation selection techniques

There are many applications in which a signal is to be recovered given measurements of its Fourier transform. However, the number of measurements that can be collected may be limited by practical considerations such as time or expense. One must then decide which samples to take. We examine the case in which the observations are selected so as to provide the best reconstruction within a specified region of interest. Optimal sampling schemes are explicitly derived for situations in which all points of the region of interest are near each other. Using this result, we find suboptimal schemes for the useful case when points of the region of interest occur in isolated clumps