Application of the Richardson-Lucy algorithm to the deconvolution of two-fold probability density functions

The authors use the Richardson-Lucy algorithm to deconvolve a set of images which are grey level representations of slices of two-fold probability density functions (PDF). These PDFs are computed from the one-dimensional signal obtained with the ESO slit-scanning infrared specklograph. In these conditions, it is shown that the PDF of the true signal is blurred by the PDF of the noise. The deconvolution is first performed on simulated data, for two levels of additive noise, i.e. for two different widths of the blurring function. These images are linked to one another, and they check the goodness of the deconvolution procedure by verifying that the properties of the image power spectrum (a quantity that can be derived from the whole set of PDF) are well conserved during the deconvolution. They discuss the quality of the result, which depends on the number of iterations. An application is made to real physical data.

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