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I try to extract woodland areas from a greyscale orthophoto. I used the "Haralick Texture Extraction" from the Orfeo Tool Box to calculate texture properties of the greyscale orthophoto. As output I get a raster with 10+ bands. Each band is representing a texture property like Contrast, Homogeneity, Dissimilarity and so on. Calculating texture properties is parameterised. You need to state a specific radius.

For the differentiation of woodland and non-woodland areas, my idea was to create a stacked raster with the texture features for 5 different radiuses, this raster would have 50+ bands, followed by a supervised classification. I already created a training dataset for woodland and non-woodland areas.

My question is: How do I identify bands of this stacked image that are relevant for the differentiation of woodland and non-woodland areas prior to the classification?

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If you want to figure out which inputs contribute largely to a classification and which offer very little, you are usually looking for a PCA ( = prinicipal component analysis).
PCA is the scientific approach to "running many possible input combinations and seeing if the results worsen/improve significantly", which you also could do manually (which is very tedious and vague).

If you search for "PCA hyperspectral", you'll find a number of approaches that can probably be applied to your use case.

If you need more specific recommendations, please provide more detail in your question (programs/code language used, data source details etc.) .

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I would recommend using a Random Forest classifier for this task for its ability to handle non-parametric data and its robustness against overfitting and outliers.

@JeffreyEvans created a utilities package for random forests called rfUtilities which may be of interest to you. The multi.collinear (p.4 documentation) command allows you to test for multicollinearity in data using qr-matrix decomposition.

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