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The painful removal of tiling
artefacts in hypersprectral data
Sevvandi Kandanaarachchi, Wil Gardner, David Alexander, Ben Muir, Philippe
Chouinard, Sheila Crewther, David Scurr, Mark Halliday, Paul Pigram
AI-OPT 2023
15-12-2023
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
Time-of-Flight
Secondary
Ion
Mass
Spectrometry
What do you get?
https://onlinelibrary.wiley.com/doi/epdf/10.1002/jex2.110
• A data cube
• 2 spatial dimensions
• 1 spectral dimension
• 10 mm x 10 mm -> 1GB data
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 (Legesse at al, 2015)
• Linear Discriminant Analysis
• Tensor Decomposition
• Linear Multiplicative method
• Simple Averaging
• Simple Interpolation
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
Candecomp/PARAFAC tensor decomposition
𝑎𝑖𝑗𝑘 ≈ 𝑥𝑖 𝑦𝑗𝑧𝑘
𝑥
𝑦
𝑧
1 component
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)
+
2 components
Tensor decomposition method
• Find the tensor decomposition of the data using 1 set of components
• The first component generally gives the tiling artefact
• So remove it
• 𝑧𝑖𝑗𝑘 = 𝑎𝑖𝑗𝑘 − 𝑥𝑖
1
𝑦𝑗
1
𝑧𝑘
1
Linear multiplicative method
• Model the noise
• In this example 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
• Using all the tiles 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 all the tiles to model it
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 – time series
seasonality
Statistical
methods
Survey
• 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 Linear Multiplicative and Seamless Stitching methods were
preferred more.
• Seamless stitching was popular for the mouse brain dataset
• No method was always supreme for all datasets– 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

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The painful removal of tiling artefacts in hypersprectral data

  • 1. The painful removal of tiling artefacts in hypersprectral data Sevvandi Kandanaarachchi, Wil Gardner, David Alexander, Ben Muir, Philippe Chouinard, Sheila Crewther, David Scurr, Mark Halliday, Paul Pigram AI-OPT 2023 15-12-2023
  • 3. What do you get? https://onlinelibrary.wiley.com/doi/epdf/10.1002/jex2.110 • A data cube • 2 spatial dimensions • 1 spectral dimension • 10 mm x 10 mm -> 1GB data
  • 4. What are tiling artefacts? A noise only portion A mouse brain sample
  • 5. 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
  • 6. 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)
  • 8. Mouse Dataset • Biological dataset • Curves • Intensity variation
  • 9. Dye and Polymer datasets • The same shape - circles • Repetition • More regular repetition in Dye compared to polymer • No intricate curves
  • 10. Resistor dataset • Same structure repeated twice • No intricate curves • Bigger tiles compared to the other datasets
  • 11. Tiling artefact removal methods • Seamless stitching (Legesse at al, 2015) • Linear Discriminant Analysis • Tensor Decomposition • Linear Multiplicative method • Simple Averaging • Simple Interpolation
  • 12. 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
  • 13. Candecomp/PARAFAC tensor decomposition 𝑎𝑖𝑗𝑘 ≈ 𝑥𝑖 𝑦𝑗𝑧𝑘 𝑥 𝑦 𝑧 1 component
  • 14. 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) + 2 components
  • 15. Tensor decomposition method • Find the tensor decomposition of the data using 1 set of components • The first component generally gives the tiling artefact • So remove it • 𝑧𝑖𝑗𝑘 = 𝑎𝑖𝑗𝑘 − 𝑥𝑖 1 𝑦𝑗 1 𝑧𝑘 1
  • 16. Linear multiplicative method • Model the noise • In this example 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
  • 17. Model • 𝑧𝑥,𝑦 = 𝑧𝑥,𝑦 × 𝑛𝑥,𝑦 • Using all the tiles 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 all the tiles to model it
  • 22. How do we evaluate these methods? • Mutual information between position and intensity • Correlation • Measure periodic nature and its reduction – time series seasonality Statistical methods Survey • 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.
  • 24. Results from the survey Rank Brain - Remove artefacts Brain - Retain information • Depending on the question asked participants selected different methods.
  • 25. Summary of results • Overall Linear Multiplicative and Seamless Stitching methods were preferred more. • Seamless stitching was popular for the mouse brain dataset • No method was always supreme for all datasets– 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.
  • 28.
  • 31. 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)
  • 32. 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
  • 33. k = 56 - more subtle
  • 35. New linear, multiplicative method A noise only portion