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Inverting a dispersive scene's side‐scanned image
Author(s) -
Harger Robert O.
Publication year - 1983
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs018i001p00083
Subject(s) - mathematics , estimator , white noise , colors of noise , noise (video) , image (mathematics) , optics , mean squared error , square (algebra) , signal (programming language) , aperture (computer memory) , colored , physics , algorithm , geometry , computer science , statistics , artificial intelligence , acoustics , materials science , composite material , programming language
Given the side‐scanned image of a scene characterized by a random, time‐varying reflectivity density, evolving in accordance with a dispersion relation, the linear, minimum mean‐square error estimator of the scene at a given time is found. The data are corrupted by additive, ‘white’ noise. The minimum mean‐square error does not depend on whether the real or the synthetic aperture technique is used or whether in the synthetic case, the ‘signal film’ or ‘complex’ image is the data. The effect of finite scanning velocity υ is to replace the white noise of spectral density η o with a ‘colored’ noise of spectral density | ‐ υ gx ( k )/υ|η o where υ gx ( k ) is the group velocity directed along υ it is assumed that υ gx ( k )/υ < 1. The anomalous behavior when υ gx ( k ) exceeds υ is noted.