Iterative reconstruction of multivariate band-limited functions from irregular sampling values
SIAM Journal on Mathematical Analysis
Analysis and design of minimax-optimal interpolators
IEEE Transactions on Signal Processing
Norm variance of minimax interpolation
IEEE Transactions on Information Theory
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Vessel mounted shallow angle LIDAR makes it possible to measure the profile of sea waves at distances up to 1km remote from the craft on which the instrument is mounted which enables a whole range of novel marine applications. However, the spatial sample locations at which the wave profiles are measured are highly non-uniformly distributed in space which renders most traditional discrete data processing techniques unusable. Consequently, in order to use the measurements it is necessary to remap the wave profile data onto an equivalent uniform sampled grid. Furthermore, to achieve the maximum range such LIDARS must operate at or near to the bare Nyquist minimum number of data points and thus local interpolation is not viable for this task. Existing non-uniform to uniform mapping methods are explored in relation to shallow angle LIDAR together with a new approach based upon transformation of the independent variable. This avoids the usual problems associated with ill conditioning that affect inversion based techniques and does not require regularisation. The discussion is illustrated using a combination of simulations and actual LIDAR wave profile measurements which are mapped onto uniform sample distributions. Effects such a wave shadowing are considered in which non-uniformities extend over several equivalent uniform steps.