Image reconstruction by neural net processor

IMAGE RECONSTRUCTION BY NEURAL NET PROCESSOR. B. Bai and N.H. Farhat, Department of Electrical Engineering, University of Pennsylvania, Philadelphia, PA 19104 It is often desired to reconstruct object functions (images) from limited frequency response data in many remote sensing applications including radar and sonar imaging. An object function f(r) in practice usually has limited extent and therefore corresponds to a Fourier transform F(p) that extends over the entire frequency space (p-space). In practice F(p) can be measured over a finite p-space only. The conventional Fourier inversion method yields an imperfect estimation f(r) of the object function and it violates a p r i o r i knowledge by assuming that F(p) outside the p-space window is zero. Retrieval of f(r) from the measured frequency' response Fd(p) is kno~l~ to be an ill-posed problem* in the sense that noise contamination and incompleteness of Fd[ p) can result in fluctuations in the object estimation. A neural net processor concept is develeped in which we set up an energy function =

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and seek its global minimum. Here T denotes the object function to be reconstructed as a state vector of the neural net; Fd is the measured frequency response over [Pl,P21; ~ is the Fourier transform of f; R(f) is a regularization function and one of the forms used is

R(f) = f {f2(r) + [ f ' ( r ) ] 2} dr and ~ is a regularization constant that controls the trade-off between smoothness and fitness of the solution. An iterative algorithm of the neural net processor is derived for object function reconstructions and its performance is evaluated digitally in the reconstruction of microwave diversity radar images from realistic data collected in an experimental imaging facility A B-52 airplane model used as test object is shown in fig. l(a) and the range-profile corresponding to zero degree aspect angle reconstructed by FFT method and by neural net processor are sho~m in fig. l(b) and fig. l(c), respectively. Range-profiles taken for a sufficient number of aspect angles are employed in image reconstruction by a filtered back-projection image algorithm. ~ The reconstruction by neural net processor reveals more features (for example the engines on the farther side of th~ fuselage) and has lower background level. Nonlinear mapping of the regularization factor in ,;~'- iterative algorithm is also introduced to make the processore more neuromorphic. Promisins results of this approach will be presented. The regularization factor can also be made adaptive to extend the role of the regularization function. The neural net processor can be implemented opto-eleetronically to achieve fast and robust reconstructions and can be easily modified for a wide range of image reconstruction applications.

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RANGE PROFILE RECONSTRUCTED RANGE-PROFILE RECONSTRUCTED BY FFT BY NEURAL NET PROCESSOR - - - ~

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A.N. Tikhonov and Y. Arsenin, I l l - P o s e d P r o b l e m , Winston, Washington, 1977. %N.H. Farhat and T.H.Chu, Proc. IOC-13, 13th Congress of the International Commission on Optics, Sapporo, Japan, 1984, pp. 62-63.

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