Image deconvolution by a logarithmic exponential nonlinear joint transform process

Claim 2

Method of recovering a substantially unsmeared image of a smeared image by performing joint transformation processing of a smeared image and its smearing function comprising the steps of: (a) producing an interference pattern between Fourier transforms of said smeared image and an image of said smearing function; (b) obtaining a joint power spectrum of said interference pattern; (c) generating the logarithm of said joint power spectrum; (d) generating the logarithm of the power spectrum of said smearing function; (e) producing a difference signal by subtracting the log of the power spectrum of said smearing function from the log of said joint power spectrum; (f) applying an inverse logarithmic function to said difference signal to produce an unsmeared joint power spectrum; and (g) Fourier transforming said unsmeared joint power spectrum to recover an unsmeared image of said smeared image.

Claim 3

Method of recovering a substantially unsmeared image of a smeared optical image by performing joint transform processing of a smeared optical image and its optical smearing function comprising the steps of: (a) displaying said smeared optical image side-by-side with said optical smearing function; (b) producing an optical interference pattern between a Fourier transform of the smeared optical image and a Fourier transform of an optical image of said smearing function; (c) obtaining a joint power spectrum of said optical interference pattern; (d) generating the logarithm of said joint power spectrum; (e) generating the logarithm of the power spectrum of said smearing function; (f) producing a difference signal by subtracting the log of the power spectrum of said smearing function from the log of said joint power spectrum; (g) applying an inverse logarithmic function to said difference signal to produce an unsmeared joint power spectrum; and (h) Fourier transforming said unsmeared joint power spectrum to recover an unsmeared image of said smeared image.

Claim 4

Method of recovering a substantially unsmeared image of a smeared optical image by performing joint transform processing of a smeared optical image and its optical smearing function comprising the steps of: (a) displaying said smeared optical image side-by-side with said optical smearing function; (b) producing an optical interference pattern between a Fourier transform of the smeared optical image and a Fourier transform of an optical image of said smearing function; (c) obtaining a joint power spectrum of said optical interference pattern; (d) generating the logarithm of said joint power spectrum; (e) generating the logarithm of the power spectrum of said smearing function; (f) producing a difference signal by subtracting the log of the power spectrum of said smearing function from the log of said joint power spectrum; (g) applying an inverse logarithmic function to said difference signal to produce an unsmeared joint power spectrum; and (h) Fourier transforming said unsmeared joint power spectrum to recover an unsmeared image of said smeared image.

Claim 5

Method of recovering a substantially unsmeared image of a smeared optical image by performing joint transform processing of a smeared optical image and an optical image of its smearing function comprising the steps of: (a) producing an optical interference pattern between a Fourier transform of the smeared optical image and a Fourier transform of the optical image of said smearing function; (b) obtaining a joint power spectrum of said optical interference pattern; (c) providing a power spectrum of said smearing function; (d) dividing the joint power spectrum of said optical interference pattern by the power spectrum of the smearing function to produce a modified joint power spectrum having the Fourier amplitude and phase of the original input signal; and (g) Fourier transforming said modified joint power spectrum to recover an unsmeared image of said smeared optical image.

Claim 6

Method of recovering a substantially unsmeared image of a smeared optical image by performing joint transform processing of a smeared optical image and an optical image of its smearing function comprising the steps of: (a) producing an optical interference pattern between a Fourier transform of the smeared optical image and a Fourier transform of the optical image of said smearing function; (b) obtaining a joint power spectrum of said optical interference pattern; (c) providing a power spectrum of said smearing function; (d) dividing the joint power spectrum of said optical interference pattern by the power spectrum of the smearing function to produce a modified joint power spectrum having the Fourier amplitude and phase of the original input signal; and (g) Fourier transforming said modified joint power spectrum to recover an unsmeared image of said smeared optical image.

Claim 7

Apparatus for recovering a substantially unsmeared image of a smeared input image by performing joint transform processing of a smeared image and its smearing function comprising: (a) means for producing an optical interference pattern between a Fourier transform of the smeared image and a Fourier transform of an optical image of said smearing function; (b) means for obtaining a joint power spectrum of said optical interference pattern; (c) means for producing the power spectrum of said smearing function; (d) means for dividing the joint power spectrum of said interference pattern by the power spectrum of the smearing function to produce a modified joint power spectrum having the Fourier amplitude and phase of the original input signal; and (g) means for Fourier transforming said modified joint power spectrum to recover an unsmeared image of said smeared input image.

Claim 8

Apparatus for recovering a substantially unsmeared image of a smeared input image by performing joint transform processing of a smeared image and its smearing function comprising: (a) means for producing an optical interference pattern between a Fourier transform of the smeared image and a Fourier transform of an optical image of said smearing function; (b) means for obtaining a joint power spectrum of said optical interference pattern; (c) means for producing the power spectrum of said smearing function; (d) means for dividing the joint power spectrum of said interference pattern by the power spectrum of the smearing function to produce a modified joint power spectrum having the Fourier amplitude and phase of the original input signal; and (g) means for Fourier transforming said modified joint power spectrum to recover an unsmeared image of said smeared input image.

Claim 9

Apparatus of claim 4 including a spatial light modulator for displaying said smeared image alongside an optical image of said smearing function and wherein said means for producing said optical interference pattern comprises a Fourier transform lens co-acting with said spatial light modulator.