Deconvolution and Denoising for Confocal Microscopy - Modeling in Computational Biology and Biomedicine - page 120

in biological systems to [ 77 , 81 ]. We will place more emphasis on developing the
“auxiliary computational supplement to the optics”, which is also the basis of many
of the super-resolution methods, and leave the classical microscope optics to the
huge number of topics and articles devoted to this subject [ 10 , 57 ]. In addition,
the resources provided at the end may serve as a starting reference for those who are
interested in developing and researching these techniques further.
Overview
Section 4.1.2 is written by keeping in mind those readers who wish to have a
first-hand understanding of the phenomenon of fluorescence, and its application to
fluorescence microscopy. The CLSM is introduced as a special case of fluorescence
microscopy, and for a better understanding, it is compared with the WFM. Image
resolution is limited primarily by noise, out-of-focus blurs and aberrations. In sim-
ple terms, blurring can be described as a non-random dispersal of light that occurs
when it passes through the entire imaging system including the sample. The image
acquisition process can be roughly divided into two parts: an optical part consisting
of the lens system and the detection part consisting of either a photodetector or a
camera. To create a faithful representation of the biological specimen, ideally, the
image acquisition process should not introduce any distortions. This of course is
almost never the case under practical conditions. When we will discuss the origin
of these distortions and make an analysis of the limiting factors in Sect. 4.2.1.2 ,
it will become clear why these distortions cannot be physically eliminated. In
Sect. 4.2.1.4 , we model this distortion process at the acquisition level, which is
known as the forward problem. One can say that the inverse problem, which is the
computational restoration of the specimen from the images, to be half-solved if the
forward problem is well modeled. We present in Sect. 4.2.2 the different challenges
that appear during a direct restoration approach and the different methodologies
that can solve this reverse problem of estimating the specimen of interest. As the
estimation process is in itself under-determined, a unique solution can be obtained
only by introducing some a priori knowledge of the system and/or the specimen. We
recall that a linear system is said to be under-determined if the number of unknowns
in the system is larger than the number of known entities. Noise can be reduced
by denoising , but in Sect. 4.2.3 we will show how it can also be contained with the
restoration process, simultaneously, by introducing some constraints on the solution
space through regularization . Case studies on the application of deconvolution are
discussed, from the literature, in Sect. 4.2.4 . Some recent ideas and developments in
this field are discussed in Sect. 4.3 along with future research challenges. Finally, we
end this chapter in Sect. 4.4 with a list of online resources on interactive tutorials,
tools, and relevant open-source/commercial softwares that we feel are most likely
to be of use. A list of the acronyms used and their expansions are provided at the
end of this chapter.