Linear And Nonlinear Problems In Fourier Imaging

Wayne M. Lawton

doi:10.1117/12.960516

Abstract

Conventional microwave and futuristic optical radar imaging requires estimating a function from limited Fourier information and a priori constraints. Linear problems include estimation from complex Fourier samples that are irregularly spaced on a polar grid (spotlight SAR), on a sinusoidal grid (laser SAR), or on a random grid (anti-aliasing phased array). Nonlinear problems include the famous phase retrieval problem of estimating a two-dimensional band limited function from its approximate Fourier modulus over a spatial region. Several deterministic and iterative methods for linear problems are described and their algorithmic complexity is discussed. A new method for attacking the infamous 'stagnation' problem that characterizes iterative methods for the phase retrieval problem is described. The method, which originated from consideration of spin-glass models of statistical lattice physics, incorporates partial information about the zero-set of the analytic continuation of the squared Fourier transform modulus in order to break the 'twin-object' symmetry responsible for stagnation.

Citation Download Citation

Wayne M. Lawton, Wayne M. Lawton, } "Linear And Nonlinear Problems In Fourier Imaging", Proc. SPIE 1101, Millimeter Wave and Synthetic Aperture Radar, (14 August 1989); doi: 10.1117/12.960516; https://doi.org/10.1117/12.960516

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