import logging
from math import ceil, log
import numpy as np
from pylops import LinearOperator
from pylops.basicoperators import Pad
try:
import pywt
except ModuleNotFoundError:
pywt = None
pywt_message = (
"Pywt package not installed. "
'Run "pip install PyWavelets" or '
'conda install pywavelets".'
)
except Exception as e:
pywt = None
pywt_message = "Failed to import pywt (error:%s)." % e
logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)
def _checkwavelet(wavelet):
"""Check that wavelet belongs to pywt.wavelist"""
wavelist = pywt.wavelist(kind="discrete")
if wavelet not in wavelist:
raise ValueError("'%s' not in family set = %s" % (wavelet, wavelist))
def _adjointwavelet(wavelet):
"""Define adjoint wavelet"""
waveletadj = wavelet
if "rbio" in wavelet:
waveletadj = "bior" + wavelet[-3:]
elif "bior" in wavelet:
waveletadj = "rbio" + wavelet[-3:]
return waveletadj
[docs]class DWT(LinearOperator):
"""One dimensional Wavelet operator.
Apply 1D-Wavelet Transform along a specific direction ``dir`` 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
https://pywavelets.readthedocs.io for a detailed description of the
input parameters.
Parameters
----------
dims : :obj:`int` or :obj:`tuple`
Number of samples for each dimension
dir : :obj:`int`, optional
Direction along which DWT 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.
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 multilevel Discrete Wavelet Transform
(DWT) in forward mode and the multilevel Inverse Discrete Wavelet Transform
(IDWT) in adjoint mode.
Wavelet transforms can be used to compress signals and present
a key advantage over Fourier transforms in that they captures both
frequency and location information in time. Consider using this operator
as sparsifying transform when using L1 solvers.
"""
def __init__(self, dims, dir=0, wavelet="haar", level=1, dtype="float64"):
if pywt is None:
raise ModuleNotFoundError(pywt_message)
_checkwavelet(wavelet)
if isinstance(dims, int):
dims = (dims,)
# define padding for length to be power of 2
ndimpow2 = max(2 ** ceil(log(dims[dir], 2)), 2 ** level)
pad = [(0, 0)] * len(dims)
pad[dir] = (0, ndimpow2 - dims[dir])
self.pad = Pad(dims, pad)
self.dims = dims
self.dir = dir
self.dimsd = list(dims)
self.dimsd[self.dir] = ndimpow2
# apply transform to find out slices
_, self.sl = pywt.coeffs_to_array(
pywt.wavedecn(
np.ones(self.dimsd),
wavelet=wavelet,
level=level,
mode="periodization",
axes=(self.dir,),
),
axes=(self.dir,),
)
self.wavelet = wavelet
self.waveletadj = _adjointwavelet(wavelet)
self.level = level
self.reshape = True if len(self.dims) > 1 else False
self.shape = (int(np.prod(self.dimsd)), int(np.prod(self.dims)))
self.dtype = np.dtype(dtype)
self.explicit = False
def _matvec(self, x):
x = self.pad.matvec(x)
if self.reshape:
x = np.reshape(x, self.dimsd)
y = pywt.coeffs_to_array(
pywt.wavedecn(
x,
wavelet=self.wavelet,
level=self.level,
mode="periodization",
axes=(self.dir,),
),
axes=(self.dir,),
)[0]
return y.ravel()
def _rmatvec(self, x):
if self.reshape:
x = np.reshape(x, self.dimsd)
x = pywt.array_to_coeffs(x, self.sl, output_format="wavedecn")
y = pywt.waverecn(
x, wavelet=self.waveletadj, mode="periodization", axes=(self.dir,)
)
y = self.pad.rmatvec(y.ravel())
return y