Resolution limits for band-limited and positivity-constrained 1-D signals

Ultimately, the band-limited nature of imaging systems restricts image quality in measured data. However, prior knowledge such as support or positivity can be employed to improve image quality beyond that available from measured data. In previous work we have shown that prior knowledge increases image quality by two means: superresolution and signal-to-noise improvements in the Fourier domain. However, after prior knowledge is enforced, the resulting filter multiplying the Fourier data may unduly limit resolution in the constrained image. In this paper, maximum achievable resolutions are derived for one-dimensional filters. It is shown that requiring a signal to be positive results in lowering its maximum achievable resolution by a factor of two. As a result, algorithms which use positivity to improve the quality of Fourier-domain data may benefit from a final post-processing step to increase resolution