一维数据中的锐步检测
sharp step detection in one-dimensional data
我的问题基本上分为两部分。我有一个一维数据集，一方面我想平滑以消除噪音，另一方面我想检测（大）数据中的步骤非常精确。
1) 关于步骤检测部分，我已经在此处找到了一个有趣的条目，但这种方法似乎不适用于我的数据。
所以我的原始数据是这样的：
enter image description here
当我应用上述方法时，结果如下：
enter image description here
2) 关于数据平滑部分，我已经尝试了一些数据平滑，例如应用 scipy 中的 gaussian_filter1d。但是当然，我的数据越平滑，检测到的步骤就越不精确（或者我在这部分有误吗？）。有没有更好的方法既能平滑数据又能保持步调清晰？
原始数据为：
[441.0, 414.0, 389.0, 430.0, 403.0, 402.0, 475.0, 417.0, 535.0, 476.0, 461.0, 415.0, 476.0, 442.0, 411.0, 422.0, 417.0, 451.0, 428.0, 455.0, 446.0, 414.0, 411.0, 413.0, 412.0, 424.0, 454.0, 439.0, 422.0, 417.0, 449.0, 417.0, 445.0, 411.0, 388.0, 420.0, 432.0, 457.0, 421.0, 415.0, 486.0, 449.0, 419.0, 453.0, 424.0, 451.0, 432.0, 464.0, 430.0, 469.0, 404.0, 461.0, 443.0, 440.0, 407.0, 452.0, 424.0, 426.0, 451.0, 423.0, 479.0, 407.0, 419.0, 435.0, 463.0, 455.0, 420.0, 413.0, 441.0, 451.0, 398.0, 433.0, 449.0, 451.0, 441.0, 450.0, 412.0, 440.0, 419.0, 408.0, 393.0, 395.0, 409.0, 450.0, 416.0, 398.0, 443.0, 403.0, 420.0, 411.0, 397.0, 416.0, 455.0, 392.0, 441.0, 422.0, 398.0, 445.0, 491.0, 405.0, 410.0, 381.0, 427.0, 403.0, 408.0, 427.0, 441.0, 464.0, 429.0, 420.0, 463.0, 405.0, 422.0, 408.0, 421.0, 464.0, 442.0, 429.0, 477.0, 407.0, 438.0, 453.0, 359.0, 435.0, 452.0, 443.0, 371.0, 503.0, 464.0, 466.0, 446.0, 465.0, 409.0, 440.0, 415.0, 384.0, 462.0, 446.0, 454.0, 440.0, 490.0, 400.0, 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非常感谢！
您可以进一步处理并检测卷积数据的局部最大值，而不仅仅是单个最大值点。
一种方法是使用 scipy.signal.find_peaks
在 的基础上，您可以添加 find_peaks 步骤，如下所示：
import numpy as np
from scipy import signal
from matplotlib import pyplot as plt
d = [ your data ]
# Convolution part
dary = np.array(d)
dary -= np.average(dary)
step = np.hstack((np.ones(len(dary)), -1*np.ones(len(dary))))
dary_step = np.convolve(dary, step, mode='valid')
# Get the peaks of the convolution
peaks = signal.find_peaks(dary_step, width=20)[0]
# plots
plt.figure()
plt.plot(dary)
plt.plot(dary_step/10)
for ii in range(len(peaks)):
plt.plot((peaks[ii], peaks[ii]), (-1500, 1500), 'r')
plt.show()
这会呈现输出：
上面的方法找到了向上的台阶，而你可以简单地使用 scipy.signal.find_peaks(-dary_step) 找到向下的台阶——正如评论中所建议的。
这是我使用工具箱 Pottslab 得到的结果
（在 Github https://github.com/mstorath/Pottslab 上）
不幸的是，它只有 Matlab，Python 还没有。
不过，如果您可以使用 Matlab，这里是简单的代码：
f = [441.0, 414.0, 389.0, 430.0, 403.0, 402.0, 475.0, 417.0, 535.0, 476.0, 461.0, 415.0, 476.0, 442.0, 411.0, 422.0, 417.0, 451.0, 428.0, 455.0, 446.0, 414.0, 411.0, 413.0, 412.0, 424.0, 454.0, 439.0, 422.0, 417.0, 449.0, 417.0, 445.0, 411.0, 388.0, 420.0, 432.0, 457.0, 421.0, 415.0, 486.0, 449.0, 419.0, 453.0, 424.0, 451.0, 432.0, 464.0, 430.0, 469.0, 404.0, 461.0, 443.0, 440.0, 407.0, 452.0, 424.0, 426.0, 451.0, 423.0, 479.0, 407.0, 419.0, 435.0, 463.0, 455.0, 420.0, 413.0, 441.0, 451.0, 398.0, 433.0, 449.0, 451.0, 441.0, 450.0, 412.0, 440.0, 419.0, 408.0, 393.0, 395.0, 409.0, 450.0, 416.0, 398.0, 443.0, 403.0, 420.0, 411.0, 397.0, 416.0, 455.0, 392.0, 441.0, 422.0, 398.0, 445.0, 491.0, 405.0, 410.0, 381.0, 427.0, 403.0, 408.0, 427.0, 441.0, 464.0, 429.0, 420.0, 463.0, 405.0, 422.0, 408.0, 421.0, 464.0, 442.0, 429.0, 477.0, 407.0, 438.0, 453.0, 359.0, 435.0, 452.0, 443.0, 371.0, 503.0, 464.0, 466.0, 446.0, 465.0, 409.0, 440.0, 415.0, 384.0, 462.0, 446.0, 454.0, 440.0, 490.0, 400.0, 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% $L^1$ Potts estimator
u = minL1Potts(f', 200);
plot(f, '-')
hold on
plot(u, '.', 'Linewidth', 2)
hold off
我的问题基本上分为两部分。我有一个一维数据集，一方面我想平滑以消除噪音，另一方面我想检测（大）数据中的步骤非常精确。
1) 关于步骤检测部分，我已经在此处找到了一个有趣的条目
所以我的原始数据是这样的： enter image description here
当我应用上述方法时，结果如下： enter image description here
2) 关于数据平滑部分，我已经尝试了一些数据平滑，例如应用 scipy 中的 gaussian_filter1d。但是当然，我的数据越平滑，检测到的步骤就越不精确（或者我在这部分有误吗？）。有没有更好的方法既能平滑数据又能保持步调清晰？
原始数据为：
[441.0, 414.0, 389.0, 430.0, 403.0, 402.0, 475.0, 417.0, 535.0, 476.0, 461.0, 415.0, 476.0, 442.0, 411.0, 422.0, 417.0, 451.0, 428.0, 455.0, 446.0, 414.0, 411.0, 413.0, 412.0, 424.0, 454.0, 439.0, 422.0, 417.0, 449.0, 417.0, 445.0, 411.0, 388.0, 420.0, 432.0, 457.0, 421.0, 415.0, 486.0, 449.0, 419.0, 453.0, 424.0, 451.0, 432.0, 464.0, 430.0, 469.0, 404.0, 461.0, 443.0, 440.0, 407.0, 452.0, 424.0, 426.0, 451.0, 423.0, 479.0, 407.0, 419.0, 435.0, 463.0, 455.0, 420.0, 413.0, 441.0, 451.0, 398.0, 433.0, 449.0, 451.0, 441.0, 450.0, 412.0, 440.0, 419.0, 408.0, 393.0, 395.0, 409.0, 450.0, 416.0, 398.0, 443.0, 403.0, 420.0, 411.0, 397.0, 416.0, 455.0, 392.0, 441.0, 422.0, 398.0, 445.0, 491.0, 405.0, 410.0, 381.0, 427.0, 403.0, 408.0, 427.0, 441.0, 464.0, 429.0, 420.0, 463.0, 405.0, 422.0, 408.0, 421.0, 464.0, 442.0, 429.0, 477.0, 407.0, 438.0, 453.0, 359.0, 435.0, 452.0, 443.0, 371.0, 503.0, 464.0, 466.0, 446.0, 465.0, 409.0, 440.0, 415.0, 384.0, 462.0, 446.0, 454.0, 440.0, 490.0, 400.0, 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非常感谢！
您可以进一步处理并检测卷积数据的局部最大值，而不仅仅是单个最大值点。
一种方法是使用 scipy.signal.find_peaks
在 find_peaks 步骤，如下所示：
import numpy as np
from scipy import signal
from matplotlib import pyplot as plt
d = [ your data ]
# Convolution part
dary = np.array(d)
dary -= np.average(dary)
step = np.hstack((np.ones(len(dary)), -1*np.ones(len(dary))))
dary_step = np.convolve(dary, step, mode='valid')
# Get the peaks of the convolution
peaks = signal.find_peaks(dary_step, width=20)[0]
# plots
plt.figure()
plt.plot(dary)
plt.plot(dary_step/10)
for ii in range(len(peaks)):
plt.plot((peaks[ii], peaks[ii]), (-1500, 1500), 'r')
plt.show()
这会呈现输出：
上面的方法找到了向上的台阶，而你可以简单地使用 scipy.signal.find_peaks(-dary_step) 找到向下的台阶——正如评论中所建议的。
这是我使用工具箱 Pottslab 得到的结果 （在 Github https://github.com/mstorath/Pottslab 上）
不幸的是，它只有 Matlab，Python 还没有。 不过，如果您可以使用 Matlab，这里是简单的代码：
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% $L^1$ Potts estimator
u = minL1Potts(f', 200);
plot(f, '-')
hold on
plot(u, '.', 'Linewidth', 2)
hold off