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Multilevel DWT, IDWT and SWT#

Multilevel DWT decomposition#

Here is an example of multilevel DWT decomposition using the db1 wavelet into approximation and detail coefficients:

import pywt
x = [3, 7, 1, 1, -2, 5, 4, 6]
db1 = pywt.Wavelet('db1')
cA3, cD3, cD2, cD1 = pywt.wavedec(x, db1)

cA3

array([8.83883476])

cD3

array([-0.35355339])

cD2

array([ 4. , -3.5])

cD1

array([-2.82842712,  0.        , -4.94974747, -1.41421356])

The number of levels in the decomposition can be determined as well:

pywt.dwt_max_level(len(x), db1)

3

or decompose to a specific level:

cA2, cD2, cD1 = pywt.wavedec(x, db1, mode='constant', level=2)

Multilevel IDWT reconstruction#

coeffs = pywt.wavedec(x, db1)
pywt.waverec(coeffs, db1)

array([ 3.,  7.,  1.,  1., -2.,  5.,  4.,  6.])

Multilevel SWT decomposition#

x = [3, 7, 1, 3, -2, 6, 4, 6]
(cA2, cD2), (cA1, cD1) = pywt.swt(x, db1, level=2)

cA1

array([7.07106781, 5.65685425, 2.82842712, 0.70710678, 2.82842712,
       7.07106781, 7.07106781, 6.36396103])

cD1

array([-2.82842712,  4.24264069, -1.41421356,  3.53553391, -5.65685425,
        1.41421356, -1.41421356,  2.12132034])

cA2

array([ 7. ,  4.5,  4. ,  5.5,  7. ,  9.5, 10. ,  8.5])

cD2

array([ 3. ,  3.5,  0. , -4.5, -3. ,  0.5,  0. ,  0.5])

[(cA2, cD2)] = pywt.swt(cA1, db1, level=1, start_level=1)

cA2

array([ 7. ,  4.5,  4. ,  5.5,  7. ,  9.5, 10. ,  8.5])

cD2

array([ 3. ,  3.5,  0. , -4.5, -3. ,  0.5,  0. ,  0.5])

coeffs = pywt.swt(x, db1)
len(coeffs)

3

pywt.swt_max_level(len(x))

3