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Allow user to set precision in CWT, increase default to 12 #570

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OverLordGoldDragon
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@OverLordGoldDragon OverLordGoldDragon commented Oct 1, 2020

Addresses this Issue. Detailed explanation here; a summary:

  1. Low precision distorts CWT, and heavily at high scales.
  2. With the L2-norm used, scales beyond 64 are increasingly distorted.
  3. Zipper-like artifacts can be seen in computed heatmaps
  4. precision=10 is low, and precision=12 does not add much computation cost, while considerably remedying 1-3.

At the least, the user should get to decide precision instead of carving it in stone. And a doc/comment should be made about these caveats.


Improvement comparison

Code
import numpy as np
import matplotlib.pyplot as plt

from pywt._extensions._pywt import DiscreteContinuousWavelet
from pywt._functions import integrate_wavelet
#%%##########################################################################
def l2(x):
    return np.sqrt(np.sum(np.abs(x ** 2)))

scales = np.power(2 ** (1 / 32), np.arange(1, 320 + 1))
wavelet = DiscreteContinuousWavelet('morl')
#%%##########################################################################
l2res = []
for precision in (10, 12, 14):
    l2res.append([])
    for scale in scales:
        int_psi, x = integrate_wavelet(wavelet, precision=precision)
        step = x[1] - x[0]
        linrange = max(x) - min(x)

        j = np.arange(scale * linrange + 1) / (scale * step)
        j = j.astype(int)  # floor
        if j[-1] >= int_psi.size:
            j = np.extract(j < int_psi.size, j)
        int_psi_scale = int_psi[j][::-1].real
        l2res[-1].append(l2(np.diff(int_psi_scale) * np.sqrt(scale)))
    
#%%##########################################################################
plt.plot(np.log2(scales), l2res[0])
plt.plot(np.log2(scales), l2res[1])
plt.plot(np.log2(scales), l2res[2])
plt.show()

@OverLordGoldDragon OverLordGoldDragon changed the title Allow user to set precision, increase default to 12 Allow user to set precision in CWT, increase default to 12 Oct 1, 2020
Higher `precision` doesn't help with lower scales
pywt/_cwt.py Show resolved Hide resolved
@grlee77
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grlee77 commented Oct 5, 2020

Thanks, I am fine with exposing this parameter.

I will take a look at the info you found soon and review it a little closer.

@OverLordGoldDragon
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OverLordGoldDragon commented Oct 8, 2020

@grlee77 Some interesting findings here (see bottom); to my surprise, pywt seems to outperform scipy on low scales. Also found a caveat2 (bottom) on integrated wavelet.

I'm curious on rationale behind integrated wavelet, which isn't documented on the site you found; perhaps it can be improved further.

amanita-citrina added a commit to amanita-citrina/pywt that referenced this pull request Oct 12, 2020
tien-vo added a commit to tien-vo/pywt that referenced this pull request Aug 13, 2024
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2 participants