In imaging situations where observations are made in spatial-frequency space, 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 from some regions of a limited-extent image. An algorithm is presented for determining which regions are recoverable and which are not for a given pattern. Noniterative recovery, analogous to that proposed by Walsh and Nielsen-Delaney [J. Opt. Soc. Am. A <b>11</b>, 572 (1994)], is shown to be feasible in cases of regular undersampling. The work has particular relevance to magnetic resonance imaging and aperture synthesis telescopy.
© 2001 Optical Society of America
(100.3020) Image processing : Image reconstruction-restoration
(100.6640) Image processing : Superresolution
(100.6950) Image processing : Tomographic image processing
(110.6960) Imaging systems : Tomography
Philip J. Bones, Nawar Alwesh, T. John Connolly, and Nicholas D. Blakeley, "Recovery of limited-extent images aliased because of spectral undersampling," J. Opt. Soc. Am. A 18, 2079-2088 (2001)