Mixing Matrix Identification using k-SCA and S3

This repository contains a novel method for identifying the mixing matrix in underdetermined blind source separation (UBSS) based on k-sparse component analysis (k-SCA). The primary goal of this method is to recover the mixing matrix A when only the mixed signals X are known, with the additional constraint that the source signals S have k-sparse columns.

Problem Statement

In UBSS, we have the following problem:

• We know the mixed signals X.
• However, both the mixing matrix A and the source signals S are unknown.
• There are more sources than sensors, making the problem underdetermined.
• The source signals S have k-sparse columns, meaning there are only k non-zero elements in each column.

Aim

The main objective of this method is to find the mixing matrix A, given the known mixed signals X and the k-sparse constraint on the source signals S.

Idea: Subspace Selective Search (S3)

This method is based on the Subspace Selective Search (S3) algorithm, which is designed to tackle the underdetermined blind source separation problem by exploiting the k-sparse nature of the source signals.

Usage

Open MATLAB.

Navigate to the code directory.

In MATLAB, run the main algorithm "Main_s3.m."

Parameters

Here are the key parameters you can configure in the code:

m: Number of sensors.

n: Number of sources.

k: Number of active sources in each time point.

T: Number of data points (samples).

Sigma: Parameter controlling the standard deviation of normal noise over zero sources.

AMode: k-SCA condition satisfaction mode.

IterNum: Number of iterations to generate a good mixing matrix.

RankTh: Threshold for generating a good mixing matrix.

MixingMode: Mixing mode ('kSCA', 'MSCA', 'PermkSCA', etc.).

Other parameters (Th, ReNum, Th1, Th2, Th3, px, alphax, hypin, Orth, etc.).

References

If you use or reference this method, please make sure to cite the following papers:

1. Multiple Sparse Component Analysis Based on Subspace Selective Search Algorithm by E. Eqlimi and B. Makkiabadi, presented at the 2015 23rd Iranian Conference on Electrical Engineering.

2. An Efficient K-SCA Based Underdetermined Channel Identification Algorithm for Online Applications by E. Eqlimi and B. Makkiabadi, presented at the 2015 23rd European Signal Processing Conference (EUSIPCO).

Contact Information

(C) Ehsan Eqlimi and Dr. Bahador Makkibadi, Jan 2015 Medical Physics & Biomedical Engineering Department Tehran University of Medical Sciences (TUMS), Tehran, Iran

For questions or inquiries, please contact:

• Dr. Ehsan Eqlimi: firstname.lastname at outlook.com
• Dr. Bahador Makkibadi