Mahotas – Reconstructing image from transformed Daubechies wavelet image

In this article we will see how we can reconstruct image from the transformed image of daubechies wavelet in mahotas. In general the Daubechies wavelets are chosen to have the highest number A of vanishing moments, (this does not imply the best smoothness) for given support width 2A. There are two naming schemes in use, DN using the length or number of taps, and dbA referring to the number of vanishing moments. So D4 and db2 are the same wavelet transform. 
In this tutorial we will use “luispedro” image, below is the command to load it. 

mahotas.demos.load('luispedro')

Below is the luispedro image 

In order to do this we will use mahotas.idaubechies method 

Syntax : mahotas.idaubechies(img, ‘D8’)
Argument : It takes image object and string i.e one of ‘D2’, ‘D4’, … ‘D20’ as argument
Return : It returns image object 

Note : Input image should be filtered or should be loaded as grey
In order to filter the image we will take the image object which is numpy.ndarray and filter it with the help of indexing, below is the command to do this

image = image[:, :, 0]

Example 1:

Python3

# importing various libraries
import numpy as np
import mahotas
import mahotas.demos
from mahotas.thresholding import soft_threshold
from pylab import imshow, show
from os import path

# loading image
f = mahotas.demos.load('luispedro', as_grey = True)



# Transform using D8 Wavelet to obtain transformed image t
t = mahotas.daubechies(f, 'D8')

# Discard low-order bits:
t /= 8
t = t.astype(np.int8)


# showing transformed image
print("Transformed Image")
imshow(t)
show()


# reconstructed image
r = mahotas.idaubechies(t, 'D8')

# showing image
print("Reconstructed Image")
imshow(r)
show()

Output :

Example 2:

Python3

# importing required libraries
import mahotas
import numpy as np
from pylab import imshow, show
import os


# loading image
img = mahotas.imread('dog_image.png')

# filtering image
img = img[:, :, 0]


# Transform using D8 Wavelet to obtain transformed image t
t = mahotas.daubechies(img, 'D8')


# showing transformed image
print("Transformed Image")
imshow(t)
show()

# reconstructed image
r = mahotas.idaubechies(t, 'D8')

# showing image
print("Reconstructed Image")
imshow(r)
show()

Output :