Three-dimensional color photon counting microscopy
using Bayesian estimation with
adaptive priori information
Myungjin Cho*
Department of Electrical, Electronic, and Control Engineering, Institute of Information Technology Convergence,
Hankyong National University, 327 Chungang-ro, Anseong-si, Kyonggi-do 456-749, Korea
*Corresponding author: mjcho@hknu.ac.kr
Received January 15, 2015; accepted May 15, 2015; posted online June 10, 2015
In this Letter, we propose a novel three-dimensional (3D) color microscopy for microorganisms under photon-
starved conditions using photon counting integral imaging and Bayesian estimation with adaptive priori infor-
mation. In photon counting integral imaging, 3D images can be visualized using maximum likelihood estimation
(MLE). However, since MLE does not consider a priori information of objects, the visual quality of 3D images
may not be accurate. In addition, the only grayscale image can be reconstructed. Therefore, to enhance the visual
quality of 3D images, we propose photon counting microscopy using maximum a posteriori with adaptive priori
information. In addition, we consider a wavelength of each basic color channel to reconstruct 3D color images. To
verify our proposed method, we carry out optical experiments.
OCIS codes: 030.5260, 100.6890, 110.6880, 170.6900.
doi: 10.3788/COL201513.070301.
Under photon-starved conditions such as low light level
environment, three-dimensional (3D) image sensing and
visualization for microorganisms have recently become a
challenging topic. In conventional microscopy, since illu-
mination devices with high-power radiation may be used
to detect the image of microorganisms, it may cause dam-
age, deformation, or destruction of the structure of 3D
microorganisms. To avoid this problem, light sources with
low-power radiation may be required. A photon counting
detector or imaging technique
[1–5]
may be applied to this
microscopy system because there are few photons in
low-power radiation. To reconstruct or visualize 3D im-
ages for microorganisms, integral imaging
[6–13]
may be used
which can obtain 3D information by capturing multiple
2D images with different perspectives through a lenslet
array or camera array. In photon counting integral
imaging, statistical estimation methods such as maximum
likelihood estimation (MLE)
[3]
or maximum a posteriori
(MAP) with fixed priori informa tion
[4]
can be used for
3D visualization. However, these estimation methods have
limitations. In MLE, since priori information is assumed to
be a uniform distribution, estimation results may be incor-
rect. In MAP with fixed priori information, all pixels of the
estimated image are related to the only fixed statistical
parameters. Thus, the estimation results may seem to
be bright or dark through the entire estimated image.
In addition, both estimation techniques can reconstruct
the only grayscale 3D images.
To solve these estimation problems, in this Letter, we
propose a novel 3D color microscopy for microorganisms
under photon-starved conditions using photon counting
integral imaging and Bayesian estimation with adaptive
priori information. We obtain the adaptive priori
information by reconstructing 3D sliced images with vari-
ous reconstruction depth planes. Then, applying MAP to
each basic color channel, we estimate more accurate 3D
color microscopy images.
A photon counting detector can be modeled statistically
by a Poisson distribution since photons occur rarely in
unit time and space
[5]
. Figure 1 illustrates a mathematical
model of a photon counting imaging system.
For computational simplicity, we use one-dimensional
notation only. To extract photons from 3D scenes in a
photon counting model, the original scene, I ðxÞ, is normal-
ized because the unit energy of the scene and the control-
lable expected number of photons ðN
p
Þ are used to
generate photons
[3,4]
. Photon generation in our statistical
model is described by the following
λðxÞ¼
I ðxÞ
P
N
x
x¼1
I ðxÞ
(1)
Fig. 1. Mathematical model of our photon counting imaging
system.
COL 13(7), 070301(2015) CHINESE OPTICS LETTERS July 10, 2015
1671-7694/2015/070301(4) 070301-1 © 2015 Chinese Optics Letters
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