与一维高斯卷积

Question

我是卷积新手，我正在使用 Python。我正在尝试将一维数组与一维高斯进行卷积，我的数组是

B = [0.011,0.022,.032,0.027,0.025,0.033,0.045,0.063,0.09,0.13,0.17,0.21]。

Gaussian 的 FWHM 是 5。所以我计算出的 sigma 是 5/2.385 = ~2.09 现在，我有 2 个选择：

使用高斯标准方程生成高斯核，并使用np.convolve(array, Gaussian) Gaussian equation I used
使用scipy.ndimage.gaussian_filter1d 由于两者都是卷积任务，理论上两者都应该给出相似的输出。但事实并非如此。为什么会这样？

我附上了一张图片，其中我绘制了阵列与另一个等距阵列的对比图

A = [1.0, 3.0, 5.0, 7.0, 9.0, 11.0, 13.0, 15.0, 17.0, 19.0, 21.0, 23.0].

The array (B) plotted against equally spaced array (A) 基本上，我想将 convolved array 和 non-convolved 数组与 A 一起绘制。我该怎么做？

Answer 1

为什么要 numpy.convolve 和 scipy.ndimage.gaussian_filter1d？

这是因为两个函数对边缘的处理不同；至少默认设置可以。如果你在中心取一个简单的峰，其他地方都为零，结果实际上是一样的（如下图所示）。默认情况下 scipy.ndimage.gaussian_filter1d 反映边缘上的数据，而 numpy.convolve 实际上用零填充数据。因此，如果在 scipy.ndimage.gaussian_filter1d 中选择 mode='constant' 默认值 cval=0 并在 mode=same 中选择 numpy.convolve 来生成类似大小的数组，结果与您一样可以看下面，一样的。

根据您要对数据执行的操作，您必须决定应如何处理边缘。

关于如何绘制这个，我希望我的示例代码解释这个。

import matplotlib.pyplot as plt
import numpy as np
from scipy.ndimage.filters import gaussian_filter1d

def gaussian( x , s):
    return 1./np.sqrt( 2. * np.pi * s**2 ) * np.exp( -x**2 / ( 2. * s**2 ) )

myData = np.zeros(25)
myData[ 12 ] = 1
myGaussian = np.fromiter( (gaussian( x , 1 ) for x in range( -3, 4, 1 ) ), np.float )
filterdData = gaussian_filter1d( myData, 1 )

myFilteredData = np.convolve( myData, myGaussian, mode='same' )
fig = plt.figure(1)

ax = fig.add_subplot( 2, 1, 1 )
ax.plot( myData, marker='x', label='peak' )
ax.plot( filterdData, marker='^',label='filter1D smeared peak' )
ax.plot( myGaussian, marker='v',label='test Gaussian' )
ax.plot( myFilteredData, marker='v', linestyle=':' ,label='convolve smeared peak' )
ax.legend( bbox_to_anchor=( 1.05, 1 ), loc=2 )

B = [0.011,0.022,.032,0.027,0.025,0.033,0.045,0.063,0.09,0.13,0.17,0.21]
myGaussian = np.fromiter( ( gaussian( x , 2.09 ) for x in range( -4, 5, 1 ) ), np.float )
bx = fig.add_subplot( 2, 1, 2 )
bx.plot( B, label='data: B' )
bx.plot( gaussian_filter1d( B, 2.09 ), label='filter1d, refl' )
bx.plot( myGaussian, label='test Gaussian' )
bx.plot(  np.convolve( B, myGaussian, mode='same' ), label='Gaussian smear' )
bx.plot( gaussian_filter1d( B, 2.09, mode='constant' ), linestyle=':', label='filter1d, constant')
bx.legend( bbox_to_anchor=(1.05, 1), loc=2 )
plt.tight_layout()
plt.show()

提供以下图片：

与一维高斯卷积

Convolution with a 1D Gaussian

python

arrays

gaussian

convolution