如何计算信号数据的点扩散函数（PSF）？答案

【问题标题】：How to calculate point spread function (PSF) for signal data?如何计算信号数据的点扩散函数（PSF）？
【发布时间】：2021-10-03 06:39:03
【问题描述】：

我在 pandas df 中有色谱数据（信号），其中一个信号处理步骤是执行峰锐化，如下图所示

参考文献如下：

文献：Paper 1(尖峰部分)Paper 2

文学中的算法

: K+1 次迭代后反卷积高分辨率数据

：点扩散函数

自适应点扩散函数估计：在正则化跟踪并称为具有标准分类的基础方法。调用的峰值用于自适应地估计局部点扩散函数 h.时间定位参数 d 是根据段中的峰间距估计。

如何找到h 的信号数据？已经关注了

PSF (point spread function) for an image (2D)

How do you extract a point spread function from a fits image?

How to build a function in Python (Jupyter) for calculation of Point Spread Function (image processing?)

所有这些都是图像数据

样本数据

Sample data
array([[ 31,  49,   1,  44],
       [ 36,  48,   0,  47],
       [ 43,  47,   0,  53],
       [ 50,  44,   0,  63],
       [ 59,  41,   0,  75],
       [ 68,  40,   1,  90],
       [ 78,  40,   6, 107],
       [ 87,  41,  12, 123],
       [ 99,  43,  20, 140],
       [110,  45,  31, 155],
       [121,  47,  42, 170],
       [131,  48,  53, 182],
       [140,  49,  63, 191],
       [148,  50,  72, 196],
       [155,  51,  79, 196],
       [161,  53,  83, 189],
       [166,  55,  83, 177],
       [169,  58,  80, 160],
       [170,  62,  72, 140],
       [167,  65,  62, 119],
       [161,  70,  51, 100],
       [154,  75,  40,  84],
       [144,  80,  30,  72],
       [132,  86,  23,  65],
       [121,  92,  19,  61],
       [111,  98,  19,  61],
       [106, 102,  23,  63],
       [105, 104,  29,  67],
       [111, 104,  38,  71],
       [123, 102,  48,  75],
       [141,  98,  59,  78],
       [160,  92,  71,  79],
       [179,  85,  85,  78],
       [195,  77, 101,  74],
       [205,  68, 117,  68],
       [208,  59, 133,  61],
       [203,  51, 145,  52],
       [191,  43, 152,  43],
       [173,  37, 154,  35],
       [150,  32, 151,  28],
       [123,  30, 142,  23],
       [ 94,  32, 129,  20],
       [ 65,  40, 114,  21],
       [ 40,  52,  96,  25],
       [ 21,  70,  77,  35],
       [  9,  91,  58,  51],
       [  1, 113,  39,  71],
       [  0, 134,  24,  97],
       [  0, 152,  13, 126],
       [  0, 168,   5, 157],
       [  0, 181,   0, 188],
       [  0, 193,   0, 216],
       [  0, 203,   0, 241],
       [  0, 211,   0, 258],
       [  0, 215,   0, 265],
       [  0, 213,   0, 262],
       [  0, 207,   0, 249],
       [  0, 195,   0, 227],
       [  0, 180,   0, 200],
       [  0, 164,   0, 170],
       [  0, 148,   0, 140],
       [  0, 132,   0, 113],
       [  0, 116,   0,  90],
       [  0, 100,   5,  74],
       [  0,  83,  18,  62],
       [  0,  66,  38,  57],
       [  0,  49,  64,  58],
       [  0,  36,  98,  64],
       [  0,  25, 133,  76],
       [  0,  18, 164,  94],
       [  0,  15, 187, 116],
       [  0,  16, 199, 143],
       [  0,  18, 199, 169],
       [  0,  22, 186, 193],
       [  1,  26, 164, 211],
       [  7,  28, 134, 222],
       [ 17,  29, 102, 224],
       [ 31,  28,  71, 218],
       [ 50,  26,  44, 204],
       [ 71,  22,  24, 184],
       [ 91,  18,  11, 160],
       [106,  13,   4, 134],
       [117,   8,   3, 109],
       [122,   5,   5,  85],
       [120,   2,  10,  64],
       [113,   0,  16,  46],
       [101,   0,  22,  32],
       [ 86,   0,  28,  22],
       [ 69,   0,  34,  16],
       [ 52,   3,  39,  13],
       [ 36,  10,  44,  13],
       [ 24,  22,  47,  18],
       [ 18,  37,  48,  25],
       [ 20,  56,  46,  36],
       [ 31,  76,  39,  49],
       [ 51,  94,  28,  63],
       [ 81, 110,  19,  75],
       [118, 123,  10,  85],
       [158, 132,   4,  90],
       [199, 136,   0,  89],
       [236, 135,   0,  84],
       [265, 131,   0,  73],
       [282, 122,   0,  59],
       [286, 110,   0,  44],
       [277,  95,   0,  29],
       [256,  79,   0,  17],
       [226,  61,   0,   8],
       [189,  44,   0,   2],
       [150,  29,   6,   0],
       [112,  17,  19,   0],
       [ 77,   8,  41,   0],
       [ 49,   3,  74,   0],
       [ 28,   0, 117,   0],
       [ 15,   0, 168,   3],
       [  7,   0, 224,  12],
       [  5,   0, 280,  28],
       [  5,   0, 333,  53],
       [  5,   0, 379,  87],
       [  5,   0, 411, 130],
       [  4,   0, 425, 178],
       [  2,   0, 419, 226],
       [  1,   0, 393, 271],
       [  0,   0, 350, 307],
       [  0,   0, 299, 329],
       [  0,   0, 248, 334],
       [  0,   0, 206, 320],
       [  0,   0, 178, 289],
       [  0,   0, 167, 246],
       [  0,   0, 173, 196],
       [  0,   0, 192, 146],
       [  0,   0, 217, 100],
       [  0,   0, 246,  61],
       [  0,   0, 275,  33],
       [  0,   0, 301,  15],
       [  0,   0, 326,   4],
       [  0,   0, 351,   0],
       [  0,   0, 377,   0],
       [  0,   0, 403,   0],
       [  0,   0, 430,   0],
       [  0,   0, 456,   0],
       [  0,   0, 484,   0],
       [  0,   0, 510,   0],
       [  0,   3, 535,   0],
       [  0,   7, 555,   0],
       [  0,  14, 569,   0],
       [  0,  22, 574,   0],
       [  0,  33, 572,   0],
       [  0,  44, 565,   0],
       [  0,  55, 555,   0],
       [  0,  66, 548,   0],
       [  1,  76, 546,   0],
       [  9,  84, 550,   0],
       [ 27,  91, 555,   0],
       [ 53,  94, 558,   0],
       [ 88,  95, 554,   0],
       [132,  94, 536,   2],
       [178,  91, 503,   7],
       [219,  86, 453,  15],
       [252,  82, 390,  24],
       [273,  77, 317,  36],
       [279,  72, 240,  44],
       [270,  69, 165,  49],
       [247,  69, 102,  48],
       [214,  73,  55,  41],
       [173,  83,  23,  30],
       [132,  98,   5,  19],
       [ 93, 121,   0,  10],
       [ 59, 150,   0,   3],
       [ 34, 186,   0,   0],
       [ 17, 227,   0,   0],
       [  6, 271,   0,   0],
       [  1, 315,   0,   0],
       [  0, 354,   0,   0],
       [  0, 384,   0,   5],
       [  0, 404,   0,  13],
       [  0, 413,   0,  25],
       [  0, 411,   0,  39],
       [  0, 398,   0,  55],
       [  0, 378,   0,  67],
       [  0, 350,   0,  75],
       [  0, 315,   0,  76],
       [  0, 276,   9,  72],
       [  0, 235,  28,  64],
       [  0, 198,  60,  53],
       [  2, 164, 107,  42],
       [ 13, 139, 172,  30],
       [ 36, 120, 242,  20],
       [ 78, 109, 310,  12],
       [143, 103, 367,   7],
       [233, 101, 404,   3],
       [344, 101, 414,   1],
       [467, 103, 394,   0],
       [591, 103, 350,   0],
       [702, 100, 287,   0],
       [786,  94, 215,   0],
       [831,  84, 144,   0],
       [833,  70,  86,   0],
       [792,  54,  44,   4],
       [713,  38,  17,  16],
       [606,  24,   4,  36]], dtype=int64)

【问题讨论】：

请发布一些示例数据
如果对数据进行傅里叶变换会发生什么 - PSF 会跳出吗？
样本数据已添加，我检查一下，我没有申请FT
您想要一个 PSF 还是四个，每列一个？
数据中有噪音吗？

标签： python pandas numpy scipy signal-processing

【解决方案1】：

感谢您发布示例数据。

首先依次对四列中的每一列进行傅立叶变换。 arr 是你上面的数据。

import numpy as np
import matplotlib.pyplot as plt

t=np.arange(0, arr.shape[0])
plt.figure()
for icol,col in enumerate(arr.T):
    sigFFT = np.fft.fft(col) / t.shape[0]
    freq = np.fft.fftfreq(t.shape[0], d=1)
    plt.plot(freq,sigFFT)

（对于没有标签等深表歉意）

您可以看到 PSF（广泛的功能）。装上信封以获得 PSF。您期待什么形状的 PSF？试试 sinc 之类的。

【讨论】：