Resolution analysis for the problem of signal recovery from finitely m
any linear measurements is the subject of this paper, The classical Ra
yleigh limit serves only as a lower bound on resolution since it does
not assume any recovery strategy and is based only on observed data. W
e show that details finer than the Rayleigh limit can be recovered by
simple linear processing that incorporates prior information, We first
define a measure of resolution based on allowable levels of error tha
t is more appropriate for current signal recovery strategies than the
Rayleigh definition, In the practical situation in which only finitely
many noisy observations are available, we have to restrict the class
of signals in order to make the resolution measure meaningful, We cons
ider the set of bandlimited and essentially timelimited signals since
it describes most signals encountered in practice. For this set, we sh
ow how to precompute resolution limits from knowledge of measurement f
unctionals, signal-to-noise ratio, passband, energy concentration regi
ons, energy concentration factor, and a prescribed level of error tole
rance, In the process, we also derive an algorithm for high-resolution
signal recovery, We illustrate the results with examples in one and t
wo dimensions.