Bandlimited Frequency-Constrained Iterative Methods

Variable aperture sampling reconstruction matrices have a history of being computationally intensive due to the need to compute a full matrix inverse. In the field of remote sensing, several spaceborne radiometers and scatterometers, which have irregular sampling and variable apertures, use iterative techniques to reconstruct measurements of the Earth’s surface. However, many of these iterative techniques tend to over-amplify noise features outside the reconstructable bandwidth. Because the reconstruction of discrete samples is inherently bandlimited, solving a bandlimited inverse can focus on recovering signal features and prevent the over-amplification of noise outside the signal bandwidth. To approximate a bandlimited inverse, we apply bandlimited constraints to several well-known iterative reconstruction techniques: Landweber iteration, additive reconstruction technique (ART), Richardson–Lucy iteration, and conjugate gradient descent. In the context of these iterative techniques, we derive an iterative method for inverting variable aperture samples, taking advantage of the regular and irregular content of variable apertures. We find that this iterative method for variable aperture reconstruction is equivalent to solving a bandlimited conjugate gradient descent algorithm.