wavelet bases

[fabian-s]

... using wavethresh?

do read up on wavelets first. also check out matt wand's code for wavelet stuff? (https://projecteuclid.org/download/pdfview_1/euclid.ejs/1323785605)

[fabian-s]

Ideally,

• [ ] as much code reuse from other tfb classes as possible
• [ ] deal with grids that are not length 2^d
• [ ] deal with irregular inputs (!)
• [ ] flexible choice of wavelet type (which?)
• [ ] (automatic) low-pass filter
• [ ] (not only use L2-loss for fitting (i.e., include transform like tfb_spline?))

Constructors for:

• [ ] data.frames
• [ ] matrix
• [ ] tfb
• [ ] tfd

[fabian-s]

umbrella issue for tidyfun/tidyfun#88 tidyfun/tidyfun#89 tidyfun/tidyfun#90 tidyfun/tidyfun#91 tidyfun/tidyfun#92

[SvenLorenz]

Choice of wavelet smoothness, primary resolution and threshold in wavelet shrinkage (Nason (2002)):

• Interpolation for non-dyadic and nonequispaced data
• LOOCV and then adapting coefficients and variance
• thresholding through variance difference between estimates
• They apparently implemented it, but i can't find code

[SvenLorenz]

I also probably found the best resource for padding: https://pywavelets.readthedocs.io/en/latest/ref/signal-extension-modes.html#modes. The implemention for wavelets in Python and it's built-in padding method.

In R it's apparently not called padding, but signal extension. The wavelets-package has a function extend.series which offers these padding methods: periodic, reflection, zeros (misspelled "zero" in the documentation), mean, and reflection.inverse.

y_nd <- c(2, 1, 4, 7, 5)
extend.series(y_nd, method = "zeros", length = "powerof2", j=3)
[1] 2 1 4 7 5 0 0 0
extend.series(y_nd, method = "periodic", length = "powerof2", j=3)
[1] 2 1 4 7 5 2 1 4
extend.series(y_nd, method = "periodic", length = "double")
 [1] 2 1 4 7 5 2 1 4 7 
extend.series(y_nd, method = "reflection", length = "powerof2", j=3)
[1] 2 1 4 7 5 5 7 4
extend.series(y_nd, method = "mean", length = "powerof2", j=3)
[1] 2.0 1.0 4.0 7.0 5.0 3.8 3.8 3.8
extend.series(y_nd, method = "reflection.inverse", length = "powerof2", j=3)
[1] 2 1 4 7 5 5 3 6

[fabian-s]

Choice of wavelet smoothness, primary resolution and threshold in wavelet shrinkage (Nason (2002)):

link goes to "Non-Dyadic Wavelet Analysis" -- intended? @SvenLorenz you showed me some other references on padding and non-dyadic data -- can you post these in the respective issues please?

The wavelets-package has a function extend.series which offers these padding methods: periodic, reflection, zeros (misspelled "zero" in the documentation), mean, and reflection.inverse.

seems easy enough to implement to avoid a dependency on another package, but sure, use that in the mean time if it fits our purpose.

[SvenLorenz]

Oh, my bad. The correct link is: https://link.springer.com/article/10.1023/A:1020746709500