Deconvolution Examples

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We present here, as part of an ongoing survey, the results of different
image restoration methods. Findings shown here have been presented at the
'Focus on Microscopy' Meeting, Heidelberg, April 1999.
Based on the work of H.Bornfleth et.al. (J.of Microscopy,189,2, pp 118-136, 1998),
a binary data set composed of 500 beads was convolved with a PSF and noise was added.
Subsequently, this data set was processed with different deconvolution
packages. Software releases available early 1999 were used. Actual implementations
might show improved performance. More quantitative data about this survey will
be made available soon.

We appreciate the support of the following individuals who contributed to this survey:


Hubert Bauch, Carl Zeiss Vision
Harald Bornfleth, (prev.) Inst.for Appl. Physics, Heidelberg
Günther Giese, MPI for Med.Research, Heidelberg
Timothey Holmes, Autoquant, Troy
Lutz Schäfer, Imaging Consultant


Data Set:



This image shows one quarter of the binary data set (256x256x32),
which is a maximum intensity projections of the stack. Simulated
beads have a volume of about 20 voxel and a diameter of about 460 nm,
sampling rate was 80x80x250 nm at an optical resolution of 360 nm.


Results I:


full size image (JPG, 8KB)

These first image shows a MIP-projection of the convolved and noise added
stack (a) and the application of Nearest Neighbors (b), Jansson-van Cittert (c)
and Least Squares deconvolutions(d).

Results II:


full size image (JPG, 8KB)

This set of images compares Maximum Entropy (CZV), and three implementations of
Maximum Likelihood (Autoquant,CZV,Imaris).


Comments:


The results document a better performance of iterative methods such as Maximum Likelihood
or Maximum Entropy over Jansson-van Cittert or Nearest Neighbors, although the computational
expense is much higher. Differences in the outcome, beside different theoretical backgrounds,
may be classified by and are due to:

-The degree of freedom programmers have when implementing these methods, such as
modeling of the PSF, SNR and background estimate, constrains, regularization.
-The degree of freedom the user has when using deconvolution, such as
sampling density, number of averages, PSF determination, number of iterations.