Abstract

The problem of reconstructing a two-dimensional function from a set of spiral samples is addressed in this paper. Our earlier research considered the special case in which the spiral samples were acquired along a linear spiral trajectory. In this paper we extend the earlier work and consider generalized, e.g., nonlinear spiral trajectories. We show that, in general, there is no exact reconstruction procedure for such trajectories. We furnish an approximate reconstruction method and bound the resulting error. Simulation results support the view that a nonlinear spiral scan has a potential advantage in a situation in which the data-collection time is limited. Such a situation arises, for example, in fast magnetic resonance imaging.

© 1988 Optical Society of America

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