Detecting patterns in waves

Question

I\'m trying to read a image from a electrocardiography and detect each one of the main waves in it (P wave, QRS complex and T wave). Now I can read the image and get a vector li

Answer 1

A piece of this puzzle is "onset detection" and a number of complex algorithms have been written to solve this problem. Here is more information on onsets.

The next piece is a Hamming Distance. This algorithms allow you to make fuzzy comparisons, the input is 2 arrays and the output is an integer "distance" or difference between the 2 data sets. The smaller the number, the more alike the 2 are. This is very close to what you need, but its not exact. I went ahead and made some modifications to the Hamming Distance algorithm to calculate a new distance, it probably has a name but i don't know what it is. Basically it adds up the absolute distance between each element in the array and returns the total. Here is the code for it in python.

import math

def absolute_distance(a1, a2, length):
       total_distance=0
       for x in range(0,length):
               total_distance+=math.fabs(a1[x]-a2[x])
       return total_distance

print(absolute_distance([1,3,9,10],[1,3,8,11],4))

This script outputs 2, which is the distance between these 2 arrays.

Now for putting together these pieces. You could use Onset detection to find the beginning of all waves in the data set. You can then loop though these location comparing each wave with a sample P-Wave. If you hit a QRS Complex the distance is going to be the largest. If you hit another P-Wave the number isn't going to be zero, but its going to be much smaller. The distance between any P-Wave and any T-Wave is going to be pretty small, HOWEVER this isn't a problem if you make the following assumption:

The distance between any p-wave and any other p-wave will be smaller than the distance between any p-wave and any t-wave.

The series looks something like this: pQtpQtpQt... The p-wave and t-wave is right next to each other, but because this sequence is predictable it will be easier to read.

On a side not, there is probably a calculus based solution to this problem. However in my mind curve fitting and integrals make this problem more of a mess. The distance function I wrote will find the area difference which is very similar subtracting the integral of both curves.

It maybe possible to sacrifice the onset calculations in favor of iterating by 1 point at a time and thus performing O(n) distance calculations, where n is the number of points in the graph. If you had a list of all of these distance calculations and knew there where 50 pQt sequences then you would know the 50 shortest distances that do not overlap where all locations of p-waves. Bingo! how is that for simplicity? However the trade off is loss of efficiency due to an increased number of distance calculations.