Deconvolution and Denoising for Confocal Microscopy - Modeling in Computational Biology and Biomedicine - page 147

deconvolution approaches [ 13 , 42 ], known as blind deconvolution, that estimate the
PSF in addition to the object intensities from the observation. As in the case of the
non-blind deconvolution algorithm, the blind approaches were developed primarily
in the field of astronomy where the blurring kernel is often unknown and cannot be
easily measured. This method was also adapted to other applications facing similar
situations. We see from Eq. ( 4.16 ) that the object and the PSF are symmetric in
the equation. So, intuitively any algorithm that estimates the object can also be
used to estimate the PSF although with different solution constraints. The blind
and non-blind algorithms assume that the PSF is shift invariant, i.e., it is the same
for every point in the specimen. In reality, as the PSF will change depending on
the specimen's optical properties, this assumption is not justified. At the very least,
it varies in depth for microscopes with large NA. In [ 28 ], the authors showed that
refractive index mismatch can result in intensity and phase variations in fluorescence
microscopy. This means that the PSF at each pixel is a little different than that of
its neighbor and an assumption of finding a universal PSF is an over-simplification.
The current deconvolution methods [ 54 ] work very well for fixed specimens but
not for live cells, because in the former case the refractive index had to be fixed to
be constant and therefore the PSF is nearly space-invariant throughout the entire
sample. More generally, the PSF can vary drastically within a living biological
sample. As a consequence, there can be a serious deterioration of image quality
particularly when deep 3-D imaging of live specimens.
To refine such data, computational methods involving space-varying deconvolu-
tion algorithms were developed. To a certain extent, these can take into account
refraction index differences within the specimen. Currently, there are no known
commercial or open-source software products that can correct the influence of
the specimen-induced aberrations on the observed image. For example, accurately
imaging the cell-components lying on the far side of a nucleus is virtually impossi-
ble without physically sectioning the sample. Nowadays, the development of more
sensitive confocal microscopes and the advent of novel deep imaging devices such
as Light Sheet based Fluorescence Microscope (LSFM), demonstrates that there is
an increasing demand, in biomedicine, for high resolution deep imaging of living
samples. Recently adaptive optics have been applied to pre-adjust the pupil phase
and thereby correct for the aberrations induced by the specimen [ 8 , 9 , 38 , 39 , 71 ].
However, to achieve this computationally, using shift-variant blind deconvolution in
3-D is quite expensive in terms of Central processing unit (CPU) memory usage and
time.
There are currently only a few libraries and toolboxes that utilize the power of
the Graphical processing unit (GPU) to ease any of the calculations. These are listed
in the next section. Apart from reducing the computational time, the iterative blind
shift-varying algorithms need to be accelerated without affecting the solution of the
optimization problem. Continued research to further refine deconvolution methods
will be key to optimize the quality of images obtained by these methods.