Biomedical Engineering Reference
In-Depth Information
Also, under non-ideal conditions, dark current flux is generated due to thermionic
emissions in the dynodes, leakage currents, field emissions, electronic emissions by
cosmic rays and sometimes stray indoor illuminations. In modern day detectors, the
dark current noise from the detector can be minimized to less than one photon per
pixel, while the normal signal levels in CLSM are 10-20 photons/pixel even for the
brighter intensities. Theoretically, a confocal image taken with 1 AU pinhole setting
has 40 % higher resolution than the image taken with WFM, but in practice, it loses
a third of its in-focus photons. The statistical noise becomes an important limitation
on the contrast and the spatial resolution [ 74 ]. Due to these reasons, in practice, a
confocal's resolution (sans deconvolution) is at best comparable, but usually lower
than the WFM! The SNR can be improved by computationally denoising the images.
If
denote the observed intensity (bounded and positive) of a
volume, for the Gaussian noise assumption, the observation model can be written as
{i (
x
):
x ∈ Ω s }
γi (
x
)= γ ( h ∗ o )(
x
)+ w (
x
) , ∀ x ∈ Ω s ,
(4.10)
(0 g ) is an Additive white Gaussian noise (AWGN) with zero
mean and variance σ g , 1 is the photon conversion factor, so that γi (
where w (
x
)
∼N
) is the
photon count at the detector. If we were to approximate a Poisson process by
a Gaussian noise, the variance of the noise will depend on the mean intensity,
γ ( h ∗ o )(
x
). As mentioned earlier in Sect. 4.2.1.2 , the high SNR case can be
addressed by employing the Central limit theorem (CLT) for large photon numbers,
where the AWGN model fits well. However, under low SNR, the AWGN model
provides a poorer description of the fluorescence microscopy imaging. In such a
case, the following Poisson model needs to be adopted:
x
γi (
x
)=
P
( γ ([ h ∗ o ](
x
)+ b (
x
))) , ∀ x ∈ Ω s ,
(4.11)
where
) denotes a voxel-wise noise function modeled as an i.i.d. Poisson process.
b : Ω s R
P
(
·
is a uniformly distributed intensity that approximates the low-frequency
background signal caused by scattered photons and autofluorescence from the
sample. The models in Eqs. ( 4.10 )and( 4.11 ) represents the forward problem of
observing the specimen, given the object, the imaging process, and a model of the
instrument.
4.2.2
Resolution and Contrast Improvement by Deconvolution
Deconvolution algorithms were initially used to increase the quality of microscopy
images by post-acquisition processing, to remove the blur and increase the image
resolution and contrast. This approach involves the mathematical inversion of the
PSF of the microscope imaging system. Although originally developed to improve
images acquired with a WFM, it was eventually realized that confocal images
could also as well benefit from deconvolution. We call the process of resolution
Search WWH ::




Custom Search