A continuously sampled object is one periodically set to zero. A continuously sampled band-limited object can be restored by multiplying by an appropriately parameterized periodic function and filtering the product. The sensitivity of this restoration procedure to additive noise is considered. In general, the restoration noise level increases dramatically as the degree of aliasing of the data increases or the duty cycle of the degradation decreases. Numerical results are given for white noise and noise with Laplace autocorrelation. The results are compared with the noise sensitivity of conventional (discrete) Shannon-sampling-theorem interpolation, in which fewer data are used.
© 1983 Optical Society of America
Robert J. Marks II and Dmitry Kaplan, "Stability of an algorithm to restore continuously sampled band-limited images from aliased data," J. Opt. Soc. Am. 73, 1518-1522 (1983)