The Blind Source Separation is a widespread problem nowadays, which has application in many fields such as picture and audio signals separation.
Abstract
The Blind Source Separation is a widespread problem nowadays, which has application in many fields such as picture and audio signals separation.
What is BSS ?
Given number of combinations of unknown source mixtures, the coefficients of the linear combination are unknown as well. Problem solution is achieved by estimating the MIXING MATRIX coefficients, and accordingly reconstructing the sources. For solving the problem algorithms such as infomax were suggested.
In this project we’ll try to improve separation results by using the sparsity of a signal.this can be achieved by performing a wavelet transform on signals;thus getting better separation results.
EEG signal separation
Multichannel electromagnetic recordings from the scalp, including EEG, magnetoencephalographic (MEG) event- related potential (ERP) and event- related field (ERF) data, have been widely used to study dynamic brain processes involved in perception memory, selective attention, recognition, and priming. However, the underlying brain processes which produce fields recorded at the scalp are largely undetermined. The most common model for EEG generation assumes that electrodes placed on the scalp surface record the electromagnetic activity of local or distributed cortical neural networks which form effective single or multiple dipole sources .
EEG recordings consist of a complex distribution of overlapping source activities, making it difficult to identify the contributing independent sources.
In this project we have data results from an EEG recordings.
here are the mathematical problem we need to solve:
we want to find the mixing matrix A, while X is mixtures vector, S the source vector,N the noise vector.
Separation using ICA and Wavelet Decomposition:
The first step was to perform a wavelet transform on the mixed signals (X(t)), getting a sparse signals, then we created a wavelet packet tree so that in every node we have quarter of the signal in the previous level (i.e if the signal size is 1024 then the next level will be 256 in each node) then we cluster the data in each node as follows:project the coefficient in each node onto a positive half sphere and perform a clustering algorithm (FCM) for ,choose a quality criteria that indicates how sparse is the signal in a specific node and accordingly this should be the best node.
After Finding the best node, ICA is used to calculate the inverse mixing matrix.
Figure 1 – Project scheme
For simulation we used 5,4,3,and 2 audio signals and in each time we added noise for both on the mixtures and the sources. First we checked the separated sources vs. SNR for 5,4,3 and 2 sources, then we calculated the the MSE(Mean Square Error) for each source inorder to compare between the original and reconstructed sources.We took the maximum MSE for each SNR among the 4 calculated MSE(for the case of separating 5,4,3,or 2) so we get the worst error we get between the sources.
– The implementation of the programs in this project is in MATLAB
– The Head Phantom was supplied by Alex & Michael Bronstien
for sensor noise:
for source noise:
Mean Square Error(MSE):
Conclusions
- As we can see from last graph of MSE(max-MSE) the result is matched to theory, meaning that the larger SNR the less we have MSE
- We saw that while adding noise at sensors, infomax was better at some cases in reconstructing signals
- While adding noise at sources, SPICA was better at reconstructing signals
- When we changed the number of sources,we saw the less sources we have the better the reconstruction is
Acknowledgment
We are grateful to our project supervisor Alex & Michael Bronstien for their help and guidance throughout this work, also to the Lab engineer Johanan Erez.
We are also grateful to the Ollendorff Minerva Center Fund for supporting this project.