Average patterns with adjacent patterns to reduce noise

[hakonanes]

Another way of reducing noise in patterns than creating model patterns from decomposition factors is by simply averaging a pattern with the adjacent patterns. This can be done by e.g. using scipy.ndimage.filters.generic_filter and passing numpy.mean as the function to apply to each pattern. There are (at least) two problems to address:

1. We cannot naively use HyperSpy's map() since we have to also access the adjacent patterns
2. If adjacent patterns are too different from the pattern to average we will increase the noise! This could be tackled by only averaging with patterns that have a low 'pattern difference', as is explained by Wright et al. (https://www.sciencedirect.com/science/article/pii/S0304399114001946). (Implementing this might be a lot of work? I don't know. Should speak to de Graef in May, since it's his work they refer to in the article.)

A s.average_patterns(num_neighbours=1) function would be nice!

[tinabe]

Comment to 2): Are you thinking about solving that by adding a conditional statement: only use pixel for averaging if the difference between them (abs of subtract) is lower than some threshold?

[hakonanes]

Yes, a suggested value should be default, however I should be able to overwrite this.

The 'pattern difference' procedure as explained by Wright et al. in the article referenced above:

1. Convert each pattern to a column vector.
2. Subtract the average intensity of each pattern from each vector component.
3. Normalise the column vector.
4. Calculate difference between two patterns by calculating the dot product between the two normalised column vectors.
5. Subtract the resulting difference value from 1 so that 0 indicates no difference and 1 represents the maximum difference.
6. Average the resulting eight difference values for each pattern to its eight adjacent patterns to obtain final difference value

[hakonanes]

Should use dask.map_overlap for this: https://docs.dask.org/en/latest/array-overlap.html#dask.array.map_overlap.

[hakonanes]

This is now possible with kikuchipy.signals.ebsd.EBSD.average_neighbour_patterns().