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2D Forward and Inverse Discrete Wavelet Transform

Single level dwt2

pywt.dwt2(data, wavelet, mode='symmetric', axes=(-2, -1))

2D Discrete Wavelet Transform.

Parameters:

data : ndarray

2D array with input data

wavelet : Wavelet object or name string

Wavelet to use

mode : str, optional

Signal extension mode, see Modes (default: ‘symmetric’)

axes : 2-tuple of ints, optional

Axes over which to compute the DWT. Repeated elements mean the DWT will be performed multiple times along these axes.
Returns:

(cA, (cH, cV, cD)) : tuple

Approximation, horizontal detail, vertical detail and diagonal detail coefficients respectively. Horizontal refers to array axis 0.

Examples

>>> import numpy as np
>>> import pywt
>>> data = np.ones((4,4), dtype=np.float64)
>>> coeffs = pywt.dwt2(data, 'haar')
>>> cA, (cH, cV, cD) = coeffs
>>> cA
array([[ 2.,  2.],
       [ 2.,  2.]])
>>> cV
array([[ 0.,  0.],
       [ 0.,  0.]])

The relation to the other common data layout where all the approximation and details coefficients are stored in one big 2D array is as follows:

                            -------------------
                            |        |        |
                            | cA(LL) | cH(LH) |
                            |        |        |
(cA, (cH, cV, cD))  <--->   -------------------
                            |        |        |
                            | cV(HL) | cD(HH) |
                            |        |        |
                            -------------------

PyWavelets does not follow this pattern because of pure practical reasons of simple access to particular type of the output coefficients.

Single level idwt2

pywt.idwt2(coeffs, wavelet, mode='symmetric', axes=(-2, -1))

2-D Inverse Discrete Wavelet Transform.

Reconstructs data from coefficient arrays.

Parameters:

coeffs : tuple

(cA, (cH, cV, cD)) A tuple with approximation coefficients and three details coefficients 2D arrays like from dwt2()

wavelet : Wavelet object or name string

Wavelet to use

mode : str, optional

Signal extension mode, see Modes (default: ‘symmetric’)

axes : 2-tuple of ints, optional

Axes over which to compute the IDWT. Repeated elements mean the IDWT will be performed multiple times along these axes.

Examples

>>> import numpy as np
>>> import pywt
>>> data = np.array([[1,2], [3,4]], dtype=np.float64)
>>> coeffs = pywt.dwt2(data, 'haar')
>>> pywt.idwt2(coeffs, 'haar')
array([[ 1.,  2.],
       [ 3.,  4.]])

2D multilevel decomposition using wavedec2

pywt.wavedec2(data, wavelet, mode='symmetric', level=None)

Multilevel 2D Discrete Wavelet Transform.

Parameters:

data : ndarray

2D input data

wavelet : Wavelet object or name string

Wavelet to use

mode : str, optional

Signal extension mode, see Modes (default: ‘symmetric’)

level : int, optional

Decomposition level (must be >= 0). If level is None (default) then it will be calculated using the dwt_max_level function.
Returns:

[cAn, (cHn, cVn, cDn), ... (cH1, cV1, cD1)] : list

Coefficients list

Examples

>>> import pywt
>>> import numpy as np
>>> coeffs = pywt.wavedec2(np.ones((4,4)), 'db1')
>>> # Levels:
>>> len(coeffs)-1
2
>>> pywt.waverec2(coeffs, 'db1')
array([[ 1.,  1.,  1.,  1.],
       [ 1.,  1.,  1.,  1.],
       [ 1.,  1.,  1.,  1.],
       [ 1.,  1.,  1.,  1.]])

2D multilevel reconstruction using waverec2

pywt.waverec2(coeffs, wavelet, mode='symmetric')

Multilevel 2D Inverse Discrete Wavelet Transform.

coeffs
: list or tuple
Coefficients list [cAn, (cHn, cVn, cDn), ... (cH1, cV1, cD1)]
wavelet
: Wavelet object or name string
Wavelet to use
mode
: str, optional
Signal extension mode, see Modes (default: ‘symmetric’)
Returns:2D array of reconstructed data.

Examples

>>> import pywt
>>> import numpy as np
>>> coeffs = pywt.wavedec2(np.ones((4,4)), 'db1')
>>> # Levels:
>>> len(coeffs)-1
2
>>> pywt.waverec2(coeffs, 'db1')
array([[ 1.,  1.,  1.,  1.],
       [ 1.,  1.,  1.,  1.],
       [ 1.,  1.,  1.,  1.],
       [ 1.,  1.,  1.,  1.]])