Image deconvolution by a logarithmic/exponential nonlinear joint transform process.

We present a nonlinear joint transform processor that uses logarithmic and exponential nonlinearities at the Fourier plane to remove the amplitude distortion effects of a smearing function. The smeared image and the blur function are displayed side by side at the input plane of the system. The exact Fourier phase of the original image is restored in the joint power spectrum from the product of the Fourier transform of the smeared image with the complex conjugate of the Fourier transform of the smearing function. The Fourier amplitude of the original image is recovered by applying the logarithmic nonlinearity to both the joint power spectrum of the smeared image and the blur function, and the Fourier spectrum of the blur function. The amplitude distortion of the joint power spectrum is then removed by subtracting the log of the Fourier spectrum of the blur function from the log of the joint power spectrum. An exponential nonlinearity is then applied to the output of the logarithmic subtraction to implement an inverse logarithmic operation and to recover the Fourier amplitude. An inverse Fourier transform operation will yield the unsmeared image at the output plane of the processor. An analysis of the logarithmic/exponential nonlinear signal processor for image deconvolution is presented. Computer simulation is presented to investigate the performance of the nonlinear processor for a linearly smeared image.