WATROO

Implements the à trous wavelet transform and associated tools: denoising, enhancement, etc.

Contents

Installation
A trous transform
Scaling functions
WOW! (Wavelets Optimized Whitening)
References

Installation

Within the active environment

pip install .

À trous transform

ATrousTransform implements a dyadic 'à-trous' transform

Scaling functions

Triangle

B3 spline

Examples

Denoise an image

import numpy as np
from watroo import AtrousTransform, Triangle

denoise_sigma = [5, 3]
transform = AtrousTransform(Triangle)
img = np.random.normal(size=(512, 512))
coefficients = transform(img, len(denoise_sigma))
# coefficients.data is an ndarray that contains the coefficients proper
coefficients.denoise(denoise_sigma)
# coeffcients accepts numpy operations
denoised = np.sum(coefficients, axis=0)
# which is equivalent to
denoised = coefficients.data.sum(axis=0)

The same result cam be obtained using the denoise convenience function

from watroo import Triangle, denoise

img = np.random.normal(size=(512, 512))
denoise_sigma = [5, 3]
denoised = denoise(img, denoise_sigma, Triangle)

Extract significant coefficients at a given scale

# return a ndarray containing the 3-sigma significance of coefficients
# at scale 2 with hard thresholding
s = coefficients.significance(3, 2, soft_threshold=False)

Compute the standard deviation of Gaussian white noise

# compute 10 scales of the 2D B3spline
w = B3spline(2)
w.compute_noise_weights(10)

This returns a 1-D ndarray containing the normalization used to estimate the significance of coefficients.

WOW! (Wavelets Optimized Whitening)

from watroo import wow
# read in your image here (must be floating point)
# ...

Standard enhancement:

wow_image, _ = wow(image)

'Bilateral' version, slower but better:

    wow_image, _ = wow(image, bilateral=1)

Denoised bilateral enhancement (best results):

wow_image, _ = wow(image, bilateral=1, denoise_coefficients=[5, 2])

References

• Starck, J.-L. & Murtagh, F. 2002, Handbook of Astronomical Data Analysis, Springer-Verlag, doi:10.1007/978-3-540-33025-7
• Auchère, F., Soubrié, E., Pelouze, G., Buchlin, É. 2022, Image Enhancement With Wavelets Optimized Whitening, A&A, 670, id.A66, doi:10.1051/0004-6361/202245345