如何平滑仅在某些部分具有大噪声的曲线？

Question

我想平滑如下所示的散点图（点非常密集），数据在这里。

曲线的中间有很大的噪声，我想使曲线平滑，而且y值也应单调增加。

由于存在许多这样的曲线，因此很难知道噪声在曲线中的位置。

我尝试过scipy.signal.savgol_filter，但是没有用。

我使用的代码是：

from scipy.signal import savgol_filter
from scipy import interpolate
import numpy as np
import matplotlib.pyplot as plt

s = np.loadtxt('data.csv', delimiter=',')
x = s[:, 0]
y = s[:, 1]
yhat = savgol_filter(y, 551, 3)

plt.plot(x, y, 'r')
plt.plot(x, yhat, 'b')
plt.show()

建议真的很感激。谢谢！

-------------------更新-------------------------

按照Colin的方法，我得到了想要的结果。这是代码：

from scipy.signal import savgol_filter
from scipy import interpolate
import numpy as np
import matplotlib.pyplot as plt

s = np.loadtxt('data.csv', delimiter=',')
x = s[:, 0]
y = s[:, 1]
yhat = savgol_filter(y, 551, 3)

tolerance = 0.2
increased_span = 150
filter_size = 11

first_pass = medfilt(y,filter_size)
diff = (y-first_pass)**2
first = np.argmax(diff>tolerance) - increased_span
last = len(y) - np.argmax(diff[::-1]>tolerance) + increased_span
print (first, last)
#interpolate between increased span
yhat[first:last] = np.interp(x[first:last], [x[first], x[last]],  [y[first], y[last]])


f = interpolate.interp1d(x, yhat, kind='slinear')
x_inter = np.linspace(x[0], x[-1], 1000)
y_inter = f(x_inter)
y_inter = savgol_filter(y_inter, 41, 3)

plt.plot(x, y, 'r')
plt.plot(x, yhat, 'b')
plt.show()

Answer 1

如果我们首先隔离故障区域，则有许多方法可以将其消除。这是一个例子：

tolerance = 0.2
increased_span = 150
filter_size = 11

#find noise
first_pass = medfilt(y,filter_size)
diff = (yhat-first_pass)**2
first = np.argmax(diff>tolerance) - increased_span
last = len(y) - np.argmax(diff[::-1]>tolerance) + increased_span

#interpolate between increased span
yhat[first:last] = np.interp(x[first:last], [x[first], x[last]],  [y[first], y[last]])