过滤/去除噪音 [英] filtering/removing noise

问题描述

问题很简单。如何去除数据中的噪音？我已经组成了一些x和y值以及一些噪声，这些噪声可以简化我正在处理的数据（除了随机噪声，我无法使其与必须处理的噪声相同）。我真的不知道我是否需要过滤或平滑。我的文件包含需要绘制的两组数据，并且该数据中存在实验噪声，删除该数据的最佳方法是什么？平滑还是过滤？

The question is simple. How do I go about removing noise from data? I have made up some x and y values along with some noise that is a gross simplification of the data I am dealing with (apart from the random noise I cannot make that the same as the noise I have to deal with). I don't really know if I need to filter or smooth. My file contains two sets of data that need to be plotted and there is experimental noise in this data, what is the best way to remove it? smoothing or filtering?

我最近将此代码发布在另一篇文章中，我所做的只是增加了噪音。

I recently posted this code in another post all I have done is added noise to it.

import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit, minimize_scalar 

x1 = [1,2,2.5,3.2,2.8,3.5,4,5]
y = [1,4,9.2,16,16.1,9.6,4,1]
noise = np.random.normal(0,1,8)
x = x1 + noise #bring on the noise

def f(x, p1, p2, p3):
return p3*(p1/((x-p2)**2 + (p1/2)**2))   

p0 = (8, 16, 0.1) # guess perameters 
plt.plot(x,y,"ro")
popt, pcov = curve_fit(f, x, y, p0)

fm = lambda x: -f(x, *popt) #this part and below is not my code but the 
#solution to my previous question     
r = minimize_scalar(fm, bounds=(1, 5))
print "maximum:", r["x"], f(r["x"], *popt)

x_curve = np.linspace(1, 5, 100)
plt.plot(x_curve, f(x_curve, *popt))
plt.plot(r['x'], f(r['x'], *popt), 'ko')
plt.show()

说我消除噪音，并用x替换x1 ...我对数据点有了很好的了解。当涉及噪音时，我该如何接近？

say I remove the noise and replace x1 with x... I get a nice fir to my data points. How can I get close to this when noise is involved?

推荐答案

使用卡尔曼滤波器消除噪音的最简单方法。假设您的数据（测量值）有些杂音。您想要使用过滤器进行校正。使用卡尔曼过滤器，并根据您的数据转换更改 transition_covariance 变量。

The easiest way to remove noises by using the Kalman filter. Let's say your data(measurement) has some noises. You want correct with a filter. Use the Kalman filter and change transition_covariance variable based on your data transition.

import matplotlib.pyplot as plt 
from pykalman import KalmanFilter 
import numpy as np

measurements = np.asarray([1, 2, 3, 5, 3, 2, 1, 2, 4, 5,7, 9, 10, 8, 5, 1]) 
kf = KalmanFilter(transition_matrices=[1],
                  observation_matrices=[1],
                  initial_state_mean=measurements[0],
                  initial_state_covariance=1,
                  observation_covariance=5,
                  transition_covariance=1) #0.01) 
state_means, state_covariances = kf.filter(measurements) 
state_std = np.sqrt(state_covariances[:,0]) 
print (state_std) 
print (state_means) 
print (state_covariances)

plt.plot(measurements, '-r', label='measurment') 
plt.plot(state_means, '-g', label='kalman-filter output') 
plt.legend(loc='upper left') 
plt.show()

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