Recovery of limited-extent images aliased because of spectral undersampling

In imaging situations where observations are made in spatial-frequency spac e, it is often desirable to lower the number of observations to fewer than that imposed by the Nyquist criterion. It is shown that patterns of regular spectral undersampling lead to aliasing that can be partially eliminated f rom some regions of a limited-extent image. An algorithm is presented for d etermining which regions are recoverable and which are not for a given patt ern. Noniterative recovery, analogous to that proposed by Walsh and Nielsen -Delaney [J. Opt. Soc. Am. A 11, 572 (1994)], is shown to be feasible in ca ses of regular undersampling. The work has particular relevance to magnetic resonance imaging and aperture synthesis telescopy. (C) 2001 Optical Socie ty of America.