Wavelet Packets

PyWavelets implements one-dimensional, two-dimensional and n-dimensional wavelet packet transform structures. The higher dimensional structures almost completely sharing programming interface with the one-dimensional tree structure.

In order to achieve this simplification, a new inheritance scheme was used in which a BaseNode base node class is a superclass for the Node, Node2D and NodeND classes.

The node classes are used as data wrappers and can be organized in trees ( binary trees for 1D transform case, quad-trees for the 2D one and 2**N-ary trees in ND). They are also superclasses to the WaveletPacket, WaveletPacket2D and WaveletPacketND classes that are used as the decomposition tree roots and contain a couple additional methods.

Here 1D, 2D and ND refer to the number of axes of the data to be transformed. All wavelet packet objects can operate on general n-dimensional arrays, but the 1D or 2D classes apply transforms along only 1 or 2 dimensions. The ND classes allow transforms over an arbitrary number of axes of n-dimensional data.

The below diagram illustrates the inheritance tree:

  • BaseNode - common interface for 1D and 2D nodes:

    • Node - data carrier node in a 1D decomposition tree

    • Node2D - data carrier node in a 2D decomposition tree

    • NodeND - data carrier node in a ND decomposition tree

BaseNode - a common interface of WaveletPacket, WaveletPacket2D and WaveletPacketND

class pywt.BaseNode

Note

The BaseNode is a base class for Node, Node2D, and NodeND. It should not be used directly unless creating a new transformation type. It is included here to document the common interface of the node and wavelet packet transform classes.

__init__(parent, data, node_name)
Parameters

  • parent – parent node. If parent is None then the node is considered detached.

  • data – The data associated with the node. An n-dimensional numeric array.

  • node_name – a name identifying the coefficients type. See Node.node_name and Node2D.node_name for information on the accepted subnodes names.

data

Data associated with the node. An n-dimensional numeric array.

parent

Parent node. Used in tree navigation. None for root node.

wavelet

Wavelet used for decomposition and reconstruction. Inherited from parent node.

axes

A tuple of ints containing the axes along which the wavelet packet transform is to be applied.

mode

Signal extension mode for the dwt() (dwt2()) and idwt() (idwt2()) decomposition and reconstruction functions. Inherited from parent node.

level

Decomposition level of the current node. 0 for root (original data), 1 for the first decomposition level, etc.

path

Path string defining position of the node in the decomposition tree.

path_tuple

A version of path, but in tuple form rather than as a single string. The tuple form is easier to work with for n-dimensional transforms. The length of the tuple will be equal to the number of levels of decomposition at the current node.

node_name

Node name describing data coefficients type of the current subnode.

See Node.node_name and Node2D.node_name.

maxlevel

Maximum allowed level of decomposition. Evaluated from parent or child nodes.

is_empty

Checks if data attribute is None.

has_any_subnode

Checks if node has any subnodes (is not a leaf node).

decompose()

Performs Discrete Wavelet Transform on the data and returns transform coefficients.

reconstruct([update=False])

Performs Inverse Discrete Wavelet Transform on subnodes coefficients and returns reconstructed data for the current level.

Parameters

update – If set, the data attribute will be updated with the reconstructed value.

Note

Descends to subnodes and recursively calls reconstruct() on them.

get_subnode(part[, decompose=True])

Returns subnode or None (see decomposition flag description).

Parameters

  • part – Subnode name

  • decompose – If True and subnode does not exist, it will be created using coefficients from the DWT decomposition of the current node.

__getitem__(path)

Used to access nodes in the decomposition tree by string path.

Parameters

path – Path string composed from valid node names. See Node.node_name and Node2D.node_name for node naming convention.

Similar to get_subnode() method with decompose=True, but can access nodes on any level in the decomposition tree.

If node does not exist yet, it will be created by decomposition of its parent node.

__setitem__(path, data)

Used to set node or node’s data in the decomposition tree. Nodes are identified by string path.

Parameters
__delitem__(path)

Used to delete node from the decomposition tree.

Parameters

path – Path string composed from valid node names. See Node.node_name and Node2D.node_name for node naming convention.

get_leaf_nodes([decompose=False])

Traverses through the decomposition tree and collects leaf nodes (nodes without any subnodes).

Parameters

decompose – If decompose is True, the method will try to decompose the tree up to the maximum level.

walk(self, func[, args=()[, kwargs={}[, decompose=True]]])

Traverses the decomposition tree and calls func(node, *args, **kwargs) on every node. If func returns True, descending to subnodes will continue.

Parameters

  • func –

    callable accepting BaseNode as the first param and optional positional and keyword arguments:

    func(node, *args, **kwargs)

  • decompose – If decompose is True (default), the method will also try to decompose the tree up to the maximum level.

Args

arguments to pass to the func

Kwargs

keyword arguments to pass to the func

walk_depth(self, func[, args=()[, kwargs={}[, decompose=False]]])

Similar to walk() but traverses the tree in depth-first order.

Parameters

  • func –

    callable accepting BaseNode as the first param and optional positional and keyword arguments:

    func(node, *args, **kwargs)

  • decompose – If decompose is True, the method will also try to decompose the tree up to the maximum level.

Args

arguments to pass to the func

Kwargs

keyword arguments to pass to the func

WaveletPacket and Node

class pywt.Node(BaseNode)
node_name

Node name describing data coefficients type of the current subnode.

For WaveletPacket case it is just as in dwt():

  • a - approximation coefficients

  • d - details coefficients

decompose()

See also

dwt() for 1D Discrete Wavelet Transform output coefficients.

reconstruct()

See also

idwt() for 1D Inverse Discrete Wavelet Transform

class pywt.WaveletPacket(Node)
__init__(data, wavelet[, mode='symmetric'[, maxlevel=None[, axis=-1]]])
Parameters

  • data – data associated with the node. N-dimensional numeric array.

  • wavelet – Wavelet to use in the transform. This can be a name of the wavelet from the wavelist() list or a Wavelet object instance.

  • mode – Signal extension mode for the dwt() and idwt() decomposition and reconstruction functions.

  • maxlevel – Maximum allowed level of decomposition. If not specified it will be calculated based on the wavelet and data length using pywt.dwt_max_level().

  • axis – The axis of the array that is to be transformed.

get_level(level[, order="natural"[, decompose=True]])

Collects nodes from the given level of decomposition.

Parameters

  • level – Specifies decomposition level from which the nodes will be collected.

  • order – Specifies nodes order - natural (natural) or frequency (freq).

  • decompose – If set then the method will try to decompose the data up to the specified level.

If nodes at the given level are missing (i.e. the tree is partially decomposed) and the decompose is set to False, only existing nodes will be returned.

reconstruct([update=True])

Reconstruct data from the subnodes.

Parameters

update – A boolean indicating whether the coefficients of the current node and its subnodes will be replaced with values from the reconstruction.

WaveletPacket2D and Node2D

class pywt.Node2D(BaseNode)
node_name
For WaveletPacket2D case it is just as in dwt2():

  • a - approximation coefficients (LL)

  • h - horizontal detail coefficients (LH)

  • v - vertical detail coefficients (HL)

  • d - diagonal detail coefficients (HH)

decompose()

See also

dwt2() for 2D Discrete Wavelet Transform output coefficients.

reconstruct()

See also

idwt2() for 2D Inverse Discrete Wavelet Transform

expand_2d_path(self, path):
class pywt.WaveletPacket2D(Node2D)
__init__(data, wavelet[, mode='symmetric'[, maxlevel=None[, axes=(-2, -1)]]])
Parameters

  • data – data associated with the node. N-dimensional numeric array.

  • wavelet – Wavelet to use in the transform. This can be a name of the wavelet from the wavelist() list or a Wavelet object instance.

  • mode – Signal extension mode for the dwt() and idwt() decomposition and reconstruction functions.

  • maxlevel – Maximum allowed level of decomposition. If not specified it will be calculated based on the wavelet and data length using pywt.dwt_max_level().

  • axes – The axes of the array that are to be transformed.

get_level(level[, order="natural"[, decompose=True]])

Collects nodes from the given level of decomposition.

Parameters

  • level – Specifies decomposition level from which the nodes will be collected.

  • order – Specifies nodes order - natural (natural) or frequency (freq).

  • decompose – If set then the method will try to decompose the data up to the specified level.

If nodes at the given level are missing (i.e. the tree is partially decomposed) and the decompose is set to False, only existing nodes will be returned.

reconstruct([update=True])

Reconstruct data from the subnodes.

Parameters

update – A boolean indicating whether the coefficients of the current node and its subnodes will be replaced with values from the reconstruction.

WaveletPacketND and NodeND

class pywt.NodeND(BaseNode)
node_name
For WaveletPacketND case it is just as in dwtn():

  • in 1D it has keys ‘a’ and ‘d’

  • in 2D it has keys ‘aa’, ‘ad’, ‘da’, ‘dd’

  • in 3D it has keys ‘aaa’, ‘aad’, ‘ada’, ‘daa’, …, ‘ddd’

decompose()

See also

dwtn() for ND Discrete Wavelet Transform output coefficients.

reconstruct()

See also

idwtn() for ND Inverse Discrete Wavelet Transform

class pywt.WaveletPacketND(NodeND)
__init__(data, wavelet[, mode='symmetric'[, maxlevel=None[, axes=None]]])
Parameters

  • data – data associated with the node. N-dimensional numeric array.

  • wavelet – Wavelet to use in the transform. This can be a name of the wavelet from the wavelist() list or a Wavelet object instance.

  • mode – Signal extension mode for the dwt() and idwt() decomposition and reconstruction functions.

  • maxlevel – Maximum allowed level of decomposition. If not specified it will be calculated based on the wavelet and data length using pywt.dwt_max_level().

  • axes – The axes of the array that are to be transformed.

get_level(level[, decompose=True])

Collects nodes from the given level of decomposition.

Parameters

  • level – Specifies decomposition level from which the nodes will be collected.

  • decompose – If set then the method will try to decompose the data up to the specified level.

If nodes at the given level are missing (i.e. the tree is partially decomposed) and the decompose is set to False, only existing nodes will be returned.

reconstruct([update=True])

Reconstruct data from the subnodes.

Parameters

update – A boolean indicating whether the coefficients of the current node and its subnodes will be replaced with values from the reconstruction.