Kriging is an estimation technique that has been proved useful in image processing since it behaves, under regular sampling, as a convolution. The uncertainty obtained with kriging has also been shown to behave as a convolution for the case of regular sampling. The convolution kernel for the uncertainty exclusively depends on the spatial correlation properties of the image. In this work we obtain, first, analytical expressions for the uncertainty of 1D images with noise using this convolution procedure. Then, we use this uncertainty to propose a new criterion for determining whether a 1D image with noise is correctly sampled.
© 2008 Optical Society of America
Original Manuscript: April 21, 2008
Revised Manuscript: October 9, 2008
Manuscript Accepted: October 23, 2008
Published: November 21, 2008
Luis Miguel Sanchez-Brea and Philip Siegmann, "Analytical determination of the uncertainty and the optimum sampling frequency for one-dimensional images with noise," Appl. Opt. 47, 6350-6356 (2008)