Deblurring in AFM images

Supervisor: Prof. Anil KokaramCo-Supervisor: Dr. David CorriganStudent: Yun feng WangDeblurring in Atomic Force Microscopy (AFM) images1Project DescriptionSFI project: collaboration with Nanoscale Function Group (NFG) in UCDThe principal measurement tool: Atomic Force Microscope (AFM) artefactsProject Target: AFM image restoration/artefacts removal2AFM 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.Briefly, the basic physical elements of the AFM consist of a laser, a photodiode and a springycantilever with a sharp tip (or probe) on it (See Fig 1.1 (a)). The tip on the cantilever is usedto scan the specimen surface. The radius of the tip is usually at the nanometer scale. The laseris used to project light onto the back of the cantilever and the photodiode is used to detect thereflected laser light. When the tip moves over the surface of the specimen (in the xy plane),changes in the surface topology and Coulomb forces (see Fig 1.1 (b)) between the tip and thesurface cause a displacement of the cantilever in the z -direction. This causes a change in thelight detected by the photodiode. The resulting change in the output of the photodiode can becorrelated to the deflection of the cantilever, and therefore to the shape of the surface.

3The Subject AFM imaging of amyloid fibrils

Approximately 20nm in diameter. In each example, slightly different copy of fibril with different brightness can be observedBlurring artefact with a dramatic form distortion which is caused by the damage of the scanning probeUse existing Bayesian deblurring algorithms in natural image domain to remove the blurring artefact in AFM images

4An Initial Guess of Blur KernelAs shown on right, a number of pixel pairs (highlighted in red) can be found with the same displacement (x, y) and intensity ratio between the fibril and its echoUse Hough Transform technique to find a set of values (x,y, ) 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) denotes the intensity ratio between the pixel intensity and its echo.

5Hough Transform (HT) Results

A slice in the Hough Space containing the bin with the highest number of votes (dark red point).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 HT resultant kernel smoothed with a 7-tap Gaussian filter.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.6Bayesian DeblurringNature Image Blur Model:Blind Deconvolution: Step1: Optimise latent image L with blur kernel k fixedThe latent image L can be optimised by finding the minimum of the function:

Solution: Fast TV-l1 Deconvolution method introduced in Xu 2010.Step2: Optimise blur kernel k with latent image L fixedNovel 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:

Solution: Rewritten as matrix multiplication form and optimised using the Conjugate Gradient (CG) based method introduced in Cho 2009.

Latent Image PriorLikelihood/NoiseBlur Kernel PriorLikelihood/Noises gradients

LimitationsThe poorly deconvolved regions in the results (regions inside red window) are the regions in which the real fibril feature overlaps with its echoesIn this scenario, the AFM imaging process is thought to obey an overwrite model rather than a summation model of convolution as assumed in our algorithmConclusion & Future WorkAs 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 algorithmThank you !