pylops.signalprocessing.DWTND

class pylops.signalprocessing.DWTND(dims, axes=(-3, -2, -1), wavelet='haar', level=1, dtype='float64', name='D')

N-dimensional Wavelet operator.

Apply ND-Wavelet transform along N 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 https://pywavelets.readthedocs.io for a detailed description of the input parameters.

Defaults to a 3D wavelet transform along the last three dimensions of the input array.

Parameters:

dimstuple

Number of samples for each dimension

axesint, optional

Axis along which DWTND is applied

waveletstr, optional

Name of wavelet type. Use pywt.wavelist(kind='discrete') for a list of available wavelets.

levelint, optional

Number of scaling levels (must be >=0).

dtypestr, optional

Type of elements in input array.

namestr, optional

Name of operator (to be used by pylops.utils.describe.describe)

Attributes:

padpylops.basicoperators.Pad

Padding operator used to pad the input signal to the next power of 2 length.

waveletadjstr

Name of the adjoint wavelet type.

sllist

List of slices to reconstruct the wavelet coefficients from the raveled array.

dimstuple

Shape of the array after the adjoint, but before flattening.

For example, x_reshaped = (Op.H * y.ravel()).reshape(Op.dims).

dimsdtuple

Shape of the array after the forward, but before flattening.

For example, y_reshaped = (Op * x.ravel()).reshape(Op.dimsd).

shapetuple

Operator shape.

Raises:

ModuleNotFoundError

If pywt is not installed

ValueError

If wavelet does not belong to pywt.families

Notes

The Wavelet operator applies the N-dimensional multilevel Discrete Wavelet Transform (DWTN) in forward mode and the N-dimensional multilevel Inverse Discrete Wavelet Transform (IDWTN) in adjoint mode.

Methods

__init__(dims[, axes, wavelet, level, ...])
adjoint()
apply_columns(cols)	Apply subset of columns of operator
cond([uselobpcg])	Condition number of linear operator.
conj()	Complex conjugate operator
div(y[, niter, densesolver])	Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(x)	Matrix-matrix or matrix-vector multiplication.
eigs([neigs, symmetric, niter, uselobpcg])	Most significant eigenvalues of linear operator.
matmat(X)	Matrix-matrix multiplication.
matvec(x)	Matrix-vector multiplication.
reset_count()	Reset counters
rmatmat(X)	Matrix-matrix multiplication.
rmatvec(x)	Adjoint matrix-vector multiplication.
todense([backend])	Return dense matrix.
toimag([forw, adj])	Imag operator
toreal([forw, adj])	Real operator
tosparse()	Return sparse matrix.
trace([neval, method, backend])	Trace of linear operator.
transpose()

Examples using pylops.signalprocessing.DWTND

Wavelet transform

Wavelet transform