Deconvolution and Denoising for Confocal Microscopy - Modeling in Computational Biology and Biomedicine - page 142

Zeiss LSM 510 fit with a 1 . 3 / 40X oil immersion lens. The voxel sizes were
(53 . 6 , 53 . 6 , 129 . 4)nm and the pinhole was set to about 33 μ m (backprojected radius
0 . 55 AU). In comparing the result of the deconvolution algorithm in Fig. 4.11 b
with the original image in Fig. 4.11 a, we can see that a significant amount of
background fluorescent was rejected after the deconvolution, even though the
sample was imaged on a confocal. There are some cytoplasmic components that
are better resolved in the images Fig. 4.11 b,dthaninFig. 4.11 a, c. From the Fourier
transforms in Fig. 4.11 e, f, we also see that there is a significant increase in the band
width (or resolution) after deconvolution.

4.2.3.2 Comments on Other Priors

In the literature, apart from TV regularization, many other methods were studied
and compared, especially when applied to fluorescence microscopy. For example,
in [ 82 , 83 ], both Gaussian and Poisson models were considered for the noise in
combination with Tikhonov, Entropy, Good's roughness regularization and also
with no regularization (ML with uniform prior). The Gaussian prior is widely used
in fluorescence imaging because it prevents noise amplifications and has excellent
convergence properties.
In [ 48 , 79 ], the authors introduced a regularization based on the 2 norm of the
gradient of the image. However, it has been observed that natural image statistics
rarely follow a 2 or Gaussian priors. In addition, 2 norms are isotropic as they
smooth the image along both the tangent and the normal to the contour surface.
In addition, from the example given in Fig. 4.9 , it was shown that the gradients of
biological specimens have heavy tailed distributions rather than Gaussian.
The images reconstructed with TV-based methods suffer from a loss in contrast.
A way to overcome is by combining the TV with an additional constraint using
for example Bregman [ 12 ] iteration. Wavelet decomposition can perform quite
well by analyzing the different scales separately in the deconvolution process.
In literature, there are many papers that are based on deconvolution of 2-D or
3-D images by using wavelets. The wavelet denoising can be substituted as a
form of regularization before or after 3-D deconvolution [ 18 , 73 ], or performed
in an optimizing context [ 31 , 84 ]. Denoising, as a pre-processing step, before
deconvolution is not recommended as the relationship between the denoised image
and the specimen is no longer related by a linear convolution operation.

4.2.4 Success Stories

In the recent edition of the Handbook of Biological Confocal Microscopy [ 57 ], the
editor Dr. James B. Pawley summarizes the main message of the handbook with
the following words: “As ever more studies are done in the field of 3-D fluorescence
microscopy, deconvolution becomes even more important for reducing the apparent