Source code for pylops.signalprocessing.dwt2d

__all__ = ["DWT2D"]

import logging
from math import ceil, log

import numpy as np

from pylops import LinearOperator
from pylops.basicoperators import Pad
from pylops.utils import deps
from pylops.utils.typing import DTypeLike, InputDimsLike, NDArray

from .dwt import _adjointwavelet, _checkwavelet

pywt_message = deps.pywt_import("the dwt2d module")

if pywt_message is None:
    import pywt

logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)

[docs]class DWT2D(LinearOperator): """Two dimensional Wavelet operator. Apply 2D-Wavelet Transform along two ``axes`` of a multi-dimensional array of size ``dims``. Note that the Wavelet operator is an overload of the ``pywt`` implementation of the wavelet transform. Refer to for a detailed description of the input parameters. Parameters ---------- dims : :obj:`tuple` Number of samples for each dimension axes : :obj:`int`, optional .. versionadded:: 2.0.0 Axis along which DWT2D is applied wavelet : :obj:`str`, optional Name of wavelet type. Use :func:`pywt.wavelist(kind='discrete')` for a list of available wavelets. level : :obj:`int`, optional Number of scaling levels (must be >=0). dtype : :obj:`str`, optional Type of elements in input array. name : :obj:`str`, optional .. versionadded:: 2.0.0 Name of operator (to be used by :func:`pylops.utils.describe.describe`) Attributes ---------- shape : :obj:`tuple` Operator shape explicit : :obj:`bool` Operator contains a matrix that can be solved explicitly (``True``) or not (``False``) Raises ------ ModuleNotFoundError If ``pywt`` is not installed ValueError If ``wavelet`` does not belong to ``pywt.families`` Notes ----- The Wavelet operator applies the 2-dimensional multilevel Discrete Wavelet Transform (DWT2) in forward mode and the 2-dimensional multilevel Inverse Discrete Wavelet Transform (IDWT2) in adjoint mode. """ def __init__( self, dims: InputDimsLike, axes: InputDimsLike = (-2, -1), wavelet: str = "haar", level: int = 1, dtype: DTypeLike = "float64", name: str = "D", ) -> None: if pywt_message is not None: raise ModuleNotFoundError(pywt_message) _checkwavelet(wavelet) # define padding for length to be power of 2 ndimpow2 = [max(2 ** ceil(log(dims[ax], 2)), 2**level) for ax in axes] pad = [(0, 0)] * len(dims) for i, ax in enumerate(axes): pad[ax] = (0, ndimpow2[i] - dims[ax]) self.pad = Pad(dims, pad) self.axes = axes dimsd = list(dims) for i, ax in enumerate(axes): dimsd[ax] = ndimpow2[i] super().__init__(dtype=np.dtype(dtype), dims=dims, dimsd=dimsd, name=name) # apply transform once again to find out slices _, = pywt.coeffs_to_array( pywt.wavedec2( np.ones(self.dimsd), wavelet=wavelet, level=level, mode="periodization", axes=self.axes, ), axes=self.axes, ) self.wavelet = wavelet self.waveletadj = _adjointwavelet(wavelet) self.level = level def _matvec(self, x: NDArray) -> NDArray: x = self.pad.matvec(x) x = np.reshape(x, self.dimsd) y = pywt.coeffs_to_array( pywt.wavedec2( x, wavelet=self.wavelet, level=self.level, mode="periodization", axes=self.axes, ), axes=(self.axes), )[0] return y.ravel() def _rmatvec(self, x: NDArray) -> NDArray: x = np.reshape(x, self.dimsd) x = pywt.array_to_coeffs(x,, output_format="wavedec2") y = pywt.waverec2( x, wavelet=self.waveletadj, mode="periodization", axes=self.axes ) y = self.pad.rmatvec(y.ravel()) return y