Deconvolution and Denoising for Confocal Microscopy - Modeling in Computational Biology and Biomedicine - page 146

4.3 Outlook

In the previous few sections, we have provided examples to show the usefulness
of the deconvolution algorithm in improving the contrast, SNR and quantitative
accuracy of chemically-fixed and living specimens. In addition, these algorithms
complement recent microscopic techniques like STED and SIM. In fact, we
recommend that deconvolution should be applied to all 3-D fluorescence microscope
images irrespective of the modality used. In spite of the enormous research base that
we have summarized above, we now highlight a few of the challenges that remain.

4.3.1 Algorithmic Developments

Since 2003, there has been many papers describing fast algorithms for minimizing
the criterion such as the one in Eq. ( 4.27 ) or those with a general norm, such as
1 norm on wavelet basis coefficients, frame coefficient, or dictionary coefficients.
1 norm promotes sparse solution as an approximation of the 0 norm which
simply counts the number of non zero coefficients. The difficulty of such a
minimization is that the first term (data term) is convex but has no Lipschitz gradient,
and that the second term (regularization) is not differentiable. In the context of
convex analysis, several fast algorithms were developed, sometimes using proximal
operators, duality, and augmented Lagrangian techniques as in [ 6 , 19 , 27 , 30 ].

4.3.2 Search for an Ideal Prior

In Sect. 4.2.3 , while we established the primordial role that prior knowledge plays
in restoring the specimen intensities, an ideal representation of the specimen does
not currently exist. In spite of the many existing priors for the specimen, there
are none that can absolutely and completely define one biological specimen and
yet be applicable to another sample. While the search for an ideal representation
of the specimen is still an open problem, in computer vision, the estimation of
the regularization parameter λ in Eq. ( 4.29 ) for non-Gaussian energy functions is
another work in progress [ 5 , 86 ].

4.3.3 Blind Shift-Varying Deconvolution

Most deconvolution software uses either a theoretical PSF (based on physical
parameters) or an empirical PSF (deduced from the specimen). There are a few