iswt2 function?

[John B]

Hello. Has anyone made progress on implementing an inverse swt2
function? It would be very helpful to have one. Any coding
suggestions?

Thanks, John

[John B]

Hello. After a few conversations with Mike Marino I was able to
create a iswt2 function. I modified Mike's iswt function slightly so
that iswt2 exactly recreates the original data used in the call to
swt2 as long as the call to swt2 used start_level=0, or it used any
start_level and either a haar or db1 wavelet. The new code is given
below. The code contains iswt2 and the modified version of Mike's
iswt.

John

---------------------------------------

import pywt
from numpy import *

def iswt(coefficients, wavelet):
"""
Input parameters:

coefficients
approx and detail coefficients, arranged in level value
exactly as output from swt:
e.g. [(cA1, cD1), (cA2, cD2), ..., (cAn, cDn)]

wavelet
Either the name of a wavelet or a Wavelet object

"""
output = coefficients[0][0].copy() # Avoid modification of input
data

#num_levels, equivalent to the decomposition level, n
num_levels = len(coefficients)
for j in range(num_levels,0,-1):
step_size = int(pow(2, j-1))
last_index = step_size
_, cD = coefficients[num_levels - j]
for first in range(last_index): # 0 to last_index - 1
# Getting the indices that we will transform
indices = arange(first, len(cD), step_size)
#print first, indices

# select the even indices
even_indices = indices[0::2]
# select the odd indices
odd_indices = indices[1::2]

# perform the inverse dwt on the selected indices,
# making sure to use periodic boundary conditions
x1 = pywt.idwt(output[even_indices], cD[even_indices], wavelet,
'per')
x2 = pywt.idwt(output[odd_indices], cD[odd_indices], wavelet,
'per')
# perform a circular shift right

# original:
#x2 = roll(x2, 1)
# average and insert into the correct indices
#output[indices] = (x1 + x2)/2.

#modified to allow exact reconstruction of original data, if
swt2 is used
# with start_level = 0, and wavelet is haar or db1
output[even_indices] = x1[0::2]
output[odd_indices] = x2[0::2]

return output



def iswt2(coefficients, wav):
"""
Input parameters:

coefficients
Approx and detail coefficients, arranged in level value
exactly as output from swt2:
e.g. [(cA_n, (cH_n, cV_n, cD_n)), (cA_n+1, (cH_n+1, cV_n+1, cD_n
+1)), ...]

Note: for accurate reconstruction of original data, swt2 must be
used with
start_level = 0, unless wavelet is haar or db1 (see modification
of iswt).

wavelet
The name of a wavelet

"""

Level = len(coefficients)
Range = range(Level)
Range.reverse()
Shape = coefficients[0][1][0].shape

Out = zeros(Shape,'d')
for iRange in Range:
C1 = coefficients[iRange]

approx = C1[0]
LL = transpose(approx)
LH = transpose(C1[1][0])
HL = transpose(C1[1][1])
HH = transpose(C1[1][2])

H = zeros(Shape,'d')
L = zeros(Shape,'d')

for i in range(H.shape[0]):
coef = [(HL[i], HH[i])]
out = iswt(coef, wav)
H[i] = out

H = H.T

for i in range(L.shape[0]):
coef = [(LL[i], LH[i])]
out = iswt(coef, wav)
L[i] = out
L = L.T

for i in range(Out.shape[0]):
coef = [(L[i], H[i])]
out = iswt(coef, wav)
Out[i] = out

return Out


---------------------------------------