Deconvolution of Laser Scanning Confocal
Microscope Volumes: Empirical
determination of the point spread function
Eyal Bar-Kochba
ENGN2500: Medical Imaging
Professor Kimia
What is a Laser Scanning Confocal
Microscopes (LSCM)?
Anatomy of the Spine
Working operation of the LSCM [1]
•
Light is captured by scanning the focused
beams of laser light across the specimen.
•
Enables the collection of true 3-D data of
specimens with multiple labels.
•
Out-of-plane light is blocked by the detector
pinhole aperture.
•
Allows visualization of deeper structures of
specimen.
•
Higher resolution than standard widefield
microscope.
Sample Images from LSCM
Highly focused images produced by LSCM [2]
LSCM image after segmentation [3]
The inherent issue with optical
microscopes: The point spread function
•
Any optical microscopes response to an object that is a point source and under the
resolution is point spread function (PSF).
•
The PSF is highly dependant on the hardware of your imaging system, e.g. objective,
imaging temperature, fluorescence color, etc…
•
Any image formed is the convolution of the object with the PSF.

Idealized PSF of a LSCM : X-Z is has worse spread
𝑑=
1.22𝜆
NA

i(r)  o(r)  psf (r) I(s)  O(s)  OTF (s)
Deconvolution mitigates blurring due to
the PSF
•
Convolution of the object with the PSF is
reversible in principle by taking the inverse FT
of the result.
•
However, due to inherent noise in the system,
the inverse FT would simply amplify the noise.
•
Also, the PSF for your specific system would
have to be accurately known for every
experiment.
Blurred Volume
Blurred Image
Restored Volume
Deconvoluted Image
Statistical determination of the PSF from
micro-fluorescent beads.
•
To deconvolve data, a good estimate
of the PSF must be known.
•
The biological specimens imaged in
the Franck Lab contained fluorescent
beads (500 nm diameters) that are
used to do Digital Volume Correlation
(DVC).
•
DVC allows us to look at the traction
forces that cells impose on there
three dimensional environment.
•
Conveniently, these Fluorescent
beads can be used to determine the
PSF of the system because they are
under the resolution of microscope.
Volume obtained used LSCM in lab. The yellow particles
are the fluorescent beads that can be seen as PSF.
Step 1: Load Volume
1. Load volume
Sample side (XZ) slice of volume
Sample top (XY) slice of volume
Step 2: Determine window size
2.
Window size was determined by sampling intensity across x – y center line + padding
Step 3: Locate beads
3.
Locate beads within volume by determining where the max intensities are located
Sample side images of nine beads
Step 3a: Filtering “bad” bead images
3a.
During search for the beads, two filters were passed
Filter 1: To filter out low intensity peaks: 𝐼𝑛𝑚𝑎𝑥 ≤ α × 𝐼𝛴𝑚𝑎𝑥
Filter 2: To filter out lumped beads: 𝐼 𝑛 − 𝛴𝐼 𝑛 ≤ 𝜖
Lumped beads
Step 4: Fit each bead
4.
Each X-Z bead image was fitted to a 2D Gaussian distribution using a Lease-Squares fit:
•
A Gaussian distribution was chosen based on “Gaussian approximations of fluorescence microscope pointspread function models.”
•
Only the X-Z was fitted because the PSF spread is worse in the X-Z:
−
𝑔( 𝑥, 𝑧 = 𝐴1 ⅇ
Nine beads before fitting
𝑥−b𝑥 2 z−b𝑧 2
− 𝜎
𝜎𝑥
𝑧
+𝒫
Nine beads after fitting
Step 5: Determine PSF
5.
Each X-Z bead image was fitted to a 2D Gaussian distribution using a Lease-Squares fit:
•
A Gaussian distribution was chosen based on “Gaussian approximations of fluorescence microscope pointspread function models.”
•
Only the X-Z was fitted because the PSF spread is worse in the X-Z:
𝑃𝑆𝐹 = 𝐴1
𝑥− b𝑥
−
𝜎𝑥
ⅇ
2
z− b𝑧
−
𝜎𝑧
2
+ 𝒫
PSF for current configuration of microscope
Step 6: Perform L-R deconvolution on
volume
•
•
PSF will be fed into an iterative based deconvolution developed by Lucy-Richardson (LR) [11]
that is implemented in MATLAB.
–
The LR deconvolution maximizes the probability that the output image that is convolved with the PSF is
an instance of the blurred image. When the best compromise between image detail enhancement and
noise has been reached, the iterations are stopped.
–
This algorithm is good in mitigating background noise the noise in the image.
–
Computationally efficient compared to other methods.
Currently the deconvolution iterates over X-Z planes and iterates ten times.
Step 6: Perform L-R deconvolution on
volume
Side slice (X-Z) before deconvolution
Side slice (X-Z) after deconvolution
Step 6: Perform L-R deconvolution on
volume
Iso-surface of beads within
subvolume before deconvolution
Iso-surface of beads within
subvolume after deconvolution
Future Work
•
Compare experimentally determined PSF to analytic solution for the PSF [7]
•
Optimized Lucy-Richardson deconvolution by determining a stop criteria
•
Perform deconvolution on volumes with cortical neurons embedded in 3D
•
Compare cellular tractions with and without deconvolution
Segmentation Using Atlas-FCM
•
[1] “Confocal Microscope” http://www.jic.ac.uk/microscopy/more/T5_8.htm
•
[2] “Microscopic and Microanalysis services”
•
[3] “Automatic Morphological Reconstruction of Neurons from Optical Imaging”
•
[4] “Image Surface: User Guide”
•
[5] “Blind deconvolution for thin-layered confocal imaging”.
•
[6] Handbook of biological confocal microscopy.
•
[7] “Gaussian approximations of fluorescence microscope point-spread function models”
•
[8] “Fast interscale wavelet denoising of Poisson-corrupted images”
•
[9] “Wavelet-based restoration methods: application to 3D confocal microscopy images”
•
[10] “REVIEW OF IMAGE DENOISING ALGORITHMS, WITH A NEW ONE∗”
•
[11] “Bayesian-Based Iterative Method of Image Restoration"