semg-decomposition

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semg-decomposition

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Implementation of surface EMG decomposition as proposed on Francesco Negro et al 2016 J. Neural Eng. 13 026027.

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# semg-decomposition

#### GUI on jupyter notebook

![semg-ui](https://user-images.githubusercontent.com/22827202/111390696-ed077180-8691-11eb-88db-2b10dd2ed326.png)

#### Progress tracking

The following algorithm is described on Negro et al. (J. Neural Engineering,
2015) - page 3:

- [x] Extend the observations x by a R factor
- [x] Subtract the mean from the observations x
- [x] Whiten x
- [x] Initialize the matrix B to empty matrix
- [x] For i = 1, 2, ..., M repeat:
 - [x] 1. Initialize the vector w\_i(0) and w\_i(-1)
 - [x] 2. While |w\_i(n)^{T}w\_i(n - 1) - 1| < Tolx 
 &nbsp;&nbsp;&nbsp;&nbsp;a. Fixed point algorithm 
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;w_i(n) = E{zg[w_i(n - 1)^{T}z]} - Aw_i(n - 1) 
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;with A = E{g'[w_i(n - 1)^{T}z]} 
 &nbsp;&nbsp;&nbsp;&nbsp;b. Orthogonalization 
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;w_i(n) = w_i(n) - BB^{T}w_i(n) 
 &nbsp;&nbsp;&nbsp;&nbsp;c. Normalization 
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;w_i(n) = w_i(n)/||w_i(n)|| 
 &nbsp;&nbsp;&nbsp;&nbsp;d. Set n = n + 1 
 - [x] 3. End while
 - [x] 4. Initialize CoV_{n - 1} and CoV\_n
 - [x] 5. While CoV\_n < CoV_{n - 1} 
 &nbsp;&nbsp;&nbsp;&nbsp;a. Estimate the i-th source 
 &nbsp;&nbsp;&nbsp;&nbsp;b. Estimate the pulse train PT_n with peak detection and K-means class 
 &nbsp;&nbsp;&nbsp;&nbsp;c. Set CoV_{n - 1} = CoV_n and calculate CoV_n of PT_n 
 &nbsp;&nbsp;&nbsp;&nbsp;d. w_i(n + 1) = (1/J) \sum_{J = 1}^{J} z(t_j) 
 &nbsp;&nbsp;&nbsp;&nbsp;e. Set n = n + 1 
 End while CoV(n) < CoV(n - 1)
 - [x] 6. If SIL > 0.9 
 &nbsp;&nbsp;&nbsp;&nbsp;a. Accept the source estimate 
 &nbsp;&nbsp;&nbsp;&nbsp;b. Add w_i to the matrix B 
 End for loop

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