Wavelet Neural Networks

pip install waveletnn

Package provides the implementation of orthonormal and biorthogonal wavelet transforms via convolutions. Batch multi-channel one- and -two-dimensional data is supported. For analysis kernels of even length are supported, while for inverse transform (synthesis) kernels are required to have length 4k + 2. The blocks are:

• OrthonormalWaveletBlock1D
• OrthonormalWaveletBlock2D
• BiorthogonalWaveletBlock1D
• BiorthogonalWaveletBlock2D
• InverseWaveletBlock1D
• InverseWaveletBlock2D

Package provides loss functions for wavelet's kernels regularizations to preserve features of both orthonormal (OrthonormalWaveletRegularization) and biorthogonal (BiorthogonalWaveletRegularization) wavelets while training. The features are admissibility (sum of coeffs), orthogonality and regularity. For more info on training see notebooks directory.

The package can use wavelets from the PyWavelets library. If the library is not yet installed use pip install waveletnn[pywt] for full installation. The wavelet blocks can be constructed by providing the name of the wavelet to be used (see pywt.wavelist()) or by manually providing scaling filter for orthonormal blocks and scaling and wavelet analysis filters for biorthogonal wavelets. Note, that results of transform blocks are different from the results of the pywt functions: the approximation from each level is half its input no matter what signal extension mode is used.

The signal extension (padding) is performed via separate module PadSequence. Extension modes are:

• "constant" -- ... v v | x1 x2 ... xn | v v ..., with default v = 0 (same as in torch, default behavior corresponds to "zero" padding in pywt)
• "circular" -- ... xn-1 xn | x1 x2 ... xn | x1 x2 ... (same as in torch, corresponds to "periodic" padding in pywt)
• "replicate" -- ... x1 x1 | x1 x2 ... xn | xn xn ... (same as in torch, corresponds to "constant" padding in pywt)
• "reflect" -- ... x3 x2 | x1 x2 ... xn | xn-1 xn-2 ... (same as in torch and pywt)
• "antireflect" -- ... (2*x1 - x3) (2*x1 - x2) | x1 x2 ... xn | (2*xn - xn-1) (2*xn - xn-2) ... (same as in pywt, not present in torch)

For examples on usage see notebooks directory.