Deconvolution of Laser Scanning Confocal Microscope Volumes: Empirical

determination of the point spread function

Eyal Bar-KochbaENGN2500: 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

LSCM image after segmentation [3]

Highly focused images produced by LSCM [2]

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.

i(r) o(r) psf (r)I(s) O(s)OTF(s)Idealized PSF of a LSCM : X-Z is has worse spread

𝑑=1.22 𝜆NA

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 Image Deconvoluted Image

Blurred Volume Restored Volume

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:

Filter 2: To filter out lumped beads:

𝐼𝑛𝑚𝑎𝑥≤α× 𝐼𝛴𝑚𝑎𝑥

⟨ 𝐼𝑛⟩− ⟨𝛴 𝐼𝑛⟩ ≤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 point-spread function models.”

• Only the X-Z was fitted because the PSF spread is worse in the X-Z:

¿Nine beads before fitting 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 point-spread function models.”

• Only the X-Z was fitted because the PSF spread is worse in the X-Z:

𝑃𝑆𝐹=⟨ 𝐴1 ⟩ⅇ−( 𝑥− ⟨b𝑥 ⟩

⟨𝜎 𝑥 ⟩ )2

−( z− ⟨b 𝑧 ⟩⟨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"