A trous wavelet transform and utilities
Project description
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
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