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
WaveletPacket
- 1D decomposition tree root node
Node2D
- data carrier node in a 2D decomposition tree
WaveletPacket2D
- 2D decomposition tree root node
NodeND
- data carrier node in a ND decomposition tree
WaveletPacketND
- ND decomposition tree root node
BaseNode - a common interface of WaveletPacket, WaveletPacket2D and WaveletPacketND¶
- class pywt.BaseNode¶
Note
The BaseNode is a base class for
Node
,Node2D
, andNodeND
. 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
andNode2D.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.
- 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()
) andidwt()
(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
andNode2D.node_name
.
- maxlevel¶
Maximum allowed level of decomposition. Evaluated from parent or child nodes.
- has_any_subnode¶
Checks if node has any subnodes (is not a leaf node).
- 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
andNode2D.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
path – Path string composed from valid node names. See
Node.node_name
andNode2D.node_name
for node naming convention.data – numeric array or
BaseNode
subclass.
- __delitem__(path)¶
Used to delete node from the decomposition tree.
- Parameters
path – Path string composed from valid node names. See
Node.node_name
andNode2D.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
isTrue
, the method will try to decompose the tree up to themaximum level
.
- walk(self, func[, args=()[, kwargs={}[, decompose=True]]])¶
Traverses the decomposition tree and calls
func(node, *args, **kwargs)
on every node. If func returnsTrue
, 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
isTrue
(default), the method will also try to decompose the tree up to themaximum 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
isTrue
, the method will also try to decompose the tree up to themaximum 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 indwt()
: a
- approximation coefficientsd
- details coefficients
- For
- 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 aWavelet
object instance.mode – Signal extension mode for the
dwt()
andidwt()
decomposition and reconstruction functions.maxlevel – Maximum allowed level of decomposition. If not specified it will be calculated based on the
wavelet
anddata
length usingpywt.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 toFalse
, 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 indwt2()
: a
- approximation coefficients (LL)h
- horizontal detail coefficients (LH)v
- vertical detail coefficients (HL)d
- diagonal detail coefficients (HH)
- For
- 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 aWavelet
object instance.mode – Signal extension mode for the
dwt()
andidwt()
decomposition and reconstruction functions.maxlevel – Maximum allowed level of decomposition. If not specified it will be calculated based on the
wavelet
anddata
length usingpywt.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 toFalse
, 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 indwtn()
: 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’
- For
- 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 aWavelet
object instance.mode – Signal extension mode for the
dwt()
andidwt()
decomposition and reconstruction functions.maxlevel – Maximum allowed level of decomposition. If not specified it will be calculated based on the
wavelet
anddata
length usingpywt.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 toFalse
, 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.