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The painful removal of tiling
artefacts in ToF-SIMS data
Sevvandi Kandanaarachchi, Wil Gardner, David Alexander, Ben Muir, Philippe
Chouinard, Sheila Crewther, David Scurr, Mark Halliday, Paul Pigram
21-11-2023
ToF-SIMS
https://serc.carleton.edu/msu_nanotech/methods/ToFSIMS.html
https://www.latrobe.edu.au/research/centres/surface/capabilities/time-of-flight-secondary-ion-mass-
spectrometry
What are tiling artefacts?
A noise only portion
A mouse brain sample
What’s the story?
• ToF-SIMS data have tiling artefacts
• We want to remove them – to make the data cleaner
• Multiple methods to remove tiling artefacts
• Didn’t pick one, instead we did a comparison study
• We did a statistical analysis and a survey
Comparison study
• 4 Datasets
• 1 biological dataset (mouse brain), 2 dye datasets, 1 resistor
• 6 Methods
• 1 tailored method for tiling removal (Seamless Stitching) – (Legesse et al,
2015)
• 3 statistical methods (LDA, tensor decomposition, linear multiplicative)
• 2 simple benchmarks (averaging and interpolating)
Datasets Mouse Brain
Polymer
Resistor
Dye
Mouse Dataset
• Biological dataset
• Curves
• Intensity variation
Dye and Polymer datasets
• The same shape - circles
• Repetition
• More regular repetition in Dye compared to
polymer
• No intricate curves
Resistor dataset
• Same structure repeated twice
• No intricate curves
• Bigger tiles compared to the other
datasets
Tiling artefact removal methods
• Seamless stitching
• Linear Discriminant Analysis
• Tensor Decomposition
• Linear Multiplicative method
• Simple Averaging
• Simple Interpolation
What is a tensor?
• Not the technical definition
• 3D data cube, or a 4D or 5D data cube
X axis
Y axis
Time
Candecomp/PARAFAC tensor decomposition
𝑎𝑖𝑗𝑘 ≈ 𝑥𝑖 𝑦𝑗𝑧𝑘
𝑥
𝑦
𝑧
Candecomp/PARAFAC tensor decomposition
𝑎𝑖𝑗𝑘 ≈ 𝑥𝑖
1
𝑦𝑗
1
𝑧𝑘
1
+ 𝑥𝑖
2
𝑦𝑗
2
𝑧𝑘
2
𝑥(1)
𝑦(1)
𝑧(1)
𝑥(2)
𝑦(2)
𝑧(2)
+
Methods
Approximate
Tiling Artefacts
and Remove
Smoothen
around Edges
Hybrid
1. Tensor Decomposition
2. LDA
3. Linear Multiplicative method
1. Simple averaging
2. Simple Interpolation
Seamless Stitching
Approximation
Original
Results –
mouse data
Dye data
Polymer
data
Resistor
data
How do we evaluate these methods?
• Mutual information between
position and intensity
• Correlation
• Measure periodic nature and
its reduction
Statistical
methods
Survey
A big thank
you all survey
participants!
• Ask two types of questions.
• How well the information was retained after
tiling artefact removal.
• How well the artefacts were removed
No standard evaluation methods in literature for ToF-SIMS tiling artefact removal.
Example
Survey
Question
Results from the survey
Rank
Brain - Remove artefacts
Brain - Retain information
• Depending on the question asked participants selected different
methods.
Summary of results
• Overall Seamless Stitching and Linear Multiplicative methods were
preferred more.
• Seamless stitching was popular for the mouse brain dataset
• No method was always supreme – No free lunch!
• Depending on the dataset characteristics, the preferred methods
were different.
• Message: caution researchers not to latch on to one method. Try out
many methods and select the best one for the dataset.
Resources
• Code:
https://github.com/sevvandi/supplementary_material/tree/master/ToF-
SIMS
• Paper: https://pubs.acs.org/doi/10.1021/acs.analchem.3c03887
Thank you!
kk = 1998
X, Y and
spectral
factors
Strong periodic signal
• In a time series context seasonality
• Time series features can capture this
• 𝑦𝑡 = 𝑓𝑡 + 𝑠𝑡 + 𝑒𝑡 (STL decomposition)
• 𝑓𝑡 - trend
• 𝑠𝑡 - seasonality
• 𝑒𝑡 - error term
• Strength of seasonality = 1 −
𝑣𝑎𝑟 𝑒𝑡
𝑣𝑎𝑟 𝑠𝑡+𝑒𝑡
• Strength of seasonality = 1 −
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓( 𝑒𝑟𝑟𝑜𝑟+𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙𝑖𝑡𝑦)
For this dataset
• We need to set the period. In this case it is 10.
• X-seasonality = 0.93
• Y-seasonality = 0.89
• There is a strong seasonal component.
• Of the remaining data if we recompute parafac and find seasonality
we get
• X-remaining-seasonality = 0.02
• Y-remaining-seasonality = 0.009
k = 56 - more subtle
k = 964
New linear, multiplicative method
A noise only portion
Model the noise – look at one tile
• Noise increases as x and y increases
• Can we model this?
• 𝑧𝑥,𝑦 = 𝑧𝑥,𝑦 × 𝑛𝑥,𝑦
• where 𝑧𝑥,𝑦 = observed value at 𝑥, 𝑦
• 𝑧𝑥,𝑦 is the true value at 𝑥, 𝑦
• 𝑛𝑥,𝑦 is the noise at 𝑥, 𝑦 is the relative position on
the tile
• 𝑥 = 𝑥 𝑚𝑜𝑑 𝑡𝑖𝑙𝑒𝑠𝑖𝑧𝑒
• 𝑦 = 𝑦 𝑚𝑜𝑑 𝑡𝑖𝑙𝑒𝑠𝑖𝑧𝑒
Model
• 𝑧𝑥,𝑦 = 𝑧𝑥,𝑦 × 𝑛𝑥,𝑦
• Model 𝑛𝑥,𝑦
• 𝑛𝑥,𝑦 = 𝑎0 + 𝑎𝑥 𝑥 + 𝑎𝑦 𝑦
• Then 𝑧𝑥,𝑦/𝑛𝑥,𝑦 = 𝑧𝑥,𝑦
• Instead of modelling using one tile, we can use several noise tiles to
model it

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The painful removal of tiling artefacts in ToF-SIMS data

  • 1. The painful removal of tiling artefacts in ToF-SIMS data Sevvandi Kandanaarachchi, Wil Gardner, David Alexander, Ben Muir, Philippe Chouinard, Sheila Crewther, David Scurr, Mark Halliday, Paul Pigram 21-11-2023
  • 3. What are tiling artefacts? A noise only portion A mouse brain sample
  • 4. What’s the story? • ToF-SIMS data have tiling artefacts • We want to remove them – to make the data cleaner • Multiple methods to remove tiling artefacts • Didn’t pick one, instead we did a comparison study • We did a statistical analysis and a survey
  • 5. Comparison study • 4 Datasets • 1 biological dataset (mouse brain), 2 dye datasets, 1 resistor • 6 Methods • 1 tailored method for tiling removal (Seamless Stitching) – (Legesse et al, 2015) • 3 statistical methods (LDA, tensor decomposition, linear multiplicative) • 2 simple benchmarks (averaging and interpolating)
  • 7. Mouse Dataset • Biological dataset • Curves • Intensity variation
  • 8. Dye and Polymer datasets • The same shape - circles • Repetition • More regular repetition in Dye compared to polymer • No intricate curves
  • 9. Resistor dataset • Same structure repeated twice • No intricate curves • Bigger tiles compared to the other datasets
  • 10. Tiling artefact removal methods • Seamless stitching • Linear Discriminant Analysis • Tensor Decomposition • Linear Multiplicative method • Simple Averaging • Simple Interpolation
  • 11. What is a tensor? • Not the technical definition • 3D data cube, or a 4D or 5D data cube X axis Y axis Time
  • 12. Candecomp/PARAFAC tensor decomposition 𝑎𝑖𝑗𝑘 ≈ 𝑥𝑖 𝑦𝑗𝑧𝑘 𝑥 𝑦 𝑧
  • 13. Candecomp/PARAFAC tensor decomposition 𝑎𝑖𝑗𝑘 ≈ 𝑥𝑖 1 𝑦𝑗 1 𝑧𝑘 1 + 𝑥𝑖 2 𝑦𝑗 2 𝑧𝑘 2 𝑥(1) 𝑦(1) 𝑧(1) 𝑥(2) 𝑦(2) 𝑧(2) +
  • 14. Methods Approximate Tiling Artefacts and Remove Smoothen around Edges Hybrid 1. Tensor Decomposition 2. LDA 3. Linear Multiplicative method 1. Simple averaging 2. Simple Interpolation Seamless Stitching Approximation Original
  • 19. How do we evaluate these methods? • Mutual information between position and intensity • Correlation • Measure periodic nature and its reduction Statistical methods Survey A big thank you all survey participants! • Ask two types of questions. • How well the information was retained after tiling artefact removal. • How well the artefacts were removed No standard evaluation methods in literature for ToF-SIMS tiling artefact removal.
  • 21. Results from the survey Rank Brain - Remove artefacts Brain - Retain information • Depending on the question asked participants selected different methods.
  • 22. Summary of results • Overall Seamless Stitching and Linear Multiplicative methods were preferred more. • Seamless stitching was popular for the mouse brain dataset • No method was always supreme – No free lunch! • Depending on the dataset characteristics, the preferred methods were different. • Message: caution researchers not to latch on to one method. Try out many methods and select the best one for the dataset.
  • 25.
  • 28. Strong periodic signal • In a time series context seasonality • Time series features can capture this • 𝑦𝑡 = 𝑓𝑡 + 𝑠𝑡 + 𝑒𝑡 (STL decomposition) • 𝑓𝑡 - trend • 𝑠𝑡 - seasonality • 𝑒𝑡 - error term • Strength of seasonality = 1 − 𝑣𝑎𝑟 𝑒𝑡 𝑣𝑎𝑟 𝑠𝑡+𝑒𝑡 • Strength of seasonality = 1 − 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓( 𝑒𝑟𝑟𝑜𝑟+𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙𝑖𝑡𝑦)
  • 29. For this dataset • We need to set the period. In this case it is 10. • X-seasonality = 0.93 • Y-seasonality = 0.89 • There is a strong seasonal component. • Of the remaining data if we recompute parafac and find seasonality we get • X-remaining-seasonality = 0.02 • Y-remaining-seasonality = 0.009
  • 30. k = 56 - more subtle
  • 32. New linear, multiplicative method A noise only portion
  • 33. Model the noise – look at one tile • Noise increases as x and y increases • Can we model this? • 𝑧𝑥,𝑦 = 𝑧𝑥,𝑦 × 𝑛𝑥,𝑦 • where 𝑧𝑥,𝑦 = observed value at 𝑥, 𝑦 • 𝑧𝑥,𝑦 is the true value at 𝑥, 𝑦 • 𝑛𝑥,𝑦 is the noise at 𝑥, 𝑦 is the relative position on the tile • 𝑥 = 𝑥 𝑚𝑜𝑑 𝑡𝑖𝑙𝑒𝑠𝑖𝑧𝑒 • 𝑦 = 𝑦 𝑚𝑜𝑑 𝑡𝑖𝑙𝑒𝑠𝑖𝑧𝑒
  • 34. Model • 𝑧𝑥,𝑦 = 𝑧𝑥,𝑦 × 𝑛𝑥,𝑦 • Model 𝑛𝑥,𝑦 • 𝑛𝑥,𝑦 = 𝑎0 + 𝑎𝑥 𝑥 + 𝑎𝑦 𝑦 • Then 𝑧𝑥,𝑦/𝑛𝑥,𝑦 = 𝑧𝑥,𝑦 • Instead of modelling using one tile, we can use several noise tiles to model it