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Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
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SVD_data_cleaning/README.md
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@ -56,6 +56,8 @@ plt.xlabel("Time [s]")
plt.ylabel("Dirty data ")
plt.show()
```
Let us look at the first three of the 100 channels.
We get three fully random time series
![figure 1](image1.png)
@ -70,4 +72,52 @@ Both combined with random mixing coefficients
## Estimating the common signal
```python
import numpy as np
import scipy
import matplotlib.pyplot as plt
file = np.load("data.npz")
clean_data = file["clean_data"]
perturbation = file["perturbation"]
dirty_data = file["dirty_data"].copy()
t: np.ndarray = np.arange(0, dirty_data.shape[0]) / 1000
dirty_data -= dirty_data.mean(axis=0, keepdims=True)
u, s, Vh = scipy.linalg.svd(dirty_data, full_matrices=False)
to_remove = u[:, 0][..., np.newaxis] * Vh[0, :][np.newaxis, ...] * s[0]
dirty_data = file["dirty_data"].copy()
dirty_data -= to_remove
for i in range(0, 3):
plt.subplot(3, 1, 1 + i)
plt.plot(t, perturbation[:, i], label="original")
plt.plot(t, to_remove[:, i], "--", label="reconstructed")
plt.xlabel("Time [s]")
plt.ylabel("Perturbation ")
plt.legend(loc="upper right")
plt.show()
for i in range(0, 3):
plt.subplot(3, 1, 1 + i)
plt.plot(t, clean_data[:, i], label="original")
plt.plot(t, dirty_data[:, i], "--", label="reconstructed")
plt.xlabel("Time [s]")
plt.ylabel("clean data waveform")
plt.legend(loc="upper right")
plt.show()
```
This is the original and the reconstructed pertubation for the first three channels
![figure 4](image4.png)
This is the original clean data and the reconstructed clean data for the first three channels
![figure 5](image5.png)