Deblurring in Atomic Force
Microscopy (AFM) images
Supervisor: Prof. Anil Kokaram
Co-Supervisor: Dr. David Corrigan
Student:Yun feng Wang
Project Description
 SFI project: collaboration with Nanoscale Function Group
(NFG) in UCD
 The principal measurement tool: Atomic Force Microscope
(AFM) – artefacts
 Project Target: AFM image restoration/artefacts removal
AFM Background
 In this project, the image data was collected under
liquid in 1mM HCL on a bespoke low noise AFM
using nanosensor SSS-NCH probes.
The Subject – AFM imaging of amyloid fibrils
 Approximately 20nm in diameter. In each example, slightly different
copy of fibril with different brightness can be observed
 Blurring artefact with a dramatic form distortion which is caused by
the damage of the scanning probe
 Use existing Bayesian deblurring algorithms in natural image domain
to remove the blurring artefact in AFM images
An Initial Guess of Blur Kernel
 As shown on right, a number of pixel pairs (highlighted
in red) can be found with the same displacement (x, y)
and intensity ratio µ between the fibril and its echo
 Use Hough Transform technique to find a set of values
(x,y, µ) which has the highest number of corresponding
pixel pairs
 The distortion in the image space was modelled using the
following equation:
 where
denotes the intensity of location (h, k)

is an echo of
offset by a vector (x, y)
 µ denotes the intensity ratio between the pixel intensity and its echo.
Hough Transform (HT) Results
By applying Hough Transform, the image is then transform into a 3-D
Hough Space. The bin with the highest number of votes denotes an initial
guess of the blur kernel.
A slice in the Hough Space containing the bin with
the highest number of votes (dark red point).
HT resultant kernel smoothed with
a 7-tap Gaussian filter.
Advantages: offers a good initial guess of blur kernel which can speed up
the convergence & help with finding the global minimum instead of local
minimum
Bayesian Deblurring
 Nature Image Blur Model:
 Blind Deconvolution:
 Step1: Optimise latent image L with blur kernel k fixed
 The latent image L can be optimised by finding the minimum of the function:
Likelihood/Noise
Latent Image Prior
 Solution: Fast TV-l1 Deconvolution method introduced in Xu 2010.
 Step2: Optimise blur kernel k with latent image L fixed
 Novel blur kernel prior: assumes the new estimated blur kernel should be sparse and
very similar to the HT blur kernel.
 The blur kernel k can be optimised by finding the minimum of the function:
Likelihood/Noise’s
gradients
Blur Kernel Prior
 Solution: Rewritten as matrix multiplication form and optimised using the
Conjugate Gradient (CG) based method introduced in Cho 2009.
Limitations
 The poorly deconvolved regions in the results (regions inside
red window) are the regions in which the real fibril feature
overlaps with its echoes
 In this scenario, the AFM imaging process is thought to obey
an overwrite model rather than a summation model of
convolution as assumed in our algorithm
Conclusion & Future Work
 As proved by the deblurring results, the proposed algorithm
is successful at removing the large distortion artefact in AFM
image. Also, the details inside the fibrils can be satisfactorily
recovered with very few artefacts.
 A direction of future work is to investigate potential
alternative ways of treating the overlap regions including
investigating the possibility of a supervised deblurring
algorithm
Thank you !