Blind-Source-Separation

This repository contains the code and documentation for the Blind Source Separation (BSS) course homework assignments. The assignments cover various topics related to BSS and its applications. Below is a summary of each homework assignment:

Homework 1

• Part A: BSS problem with linear and instantaneous Sources

  

• Part B: Steepest Descend, Newton's Method, Alternation Minimization, Gradient Projection

  

Homework 2

• Part A: Principal Component Analysis (PCA) - Singular Value Decomposition (SVD)

• Part B: Beamforming - Multiple Signal Classification (MUSIC)

  

Homework 3

• Part A: Common Spatial Patterns (CSP) combined with Linear Discriminant Analysis (LDA) for motion classification using EEG Signal

  

• Part B: Canonical Correlation Analysis (CCA) for identifying the Steady-State Visually Evoked Potential (SSVEP) frequency

  

Homework 4

• Part A: BSS poblem with non stationary uncorrelated sources

  

• Part B: BSS problem with mutually uncorolated sources

Homework 5

• Sparse recovery problem with different methods:
  • Subset selection
  • Matching Pursuit (MP)
  • Orthogonal Matching Pursuit (OMP)
  • Basis Pursuit (BP)
  • Iteratively Reweighted Least Square (IRLS)

Homework 6

• Part A: Least Absolute Shrinkage and Selection Operator (LASSO)

• Part B: 2d and 3d frame designing

  

• Part C: K-SVD and MOD for sparse signal recovery (dictionary learning)

  

Homework 7

• Single & multi-channel sparse blind deconvolution

  

Homework 8

• BSS problem with independent sources, minimize the Kullback-Leibler divergence (D_kl)

  

Homework 9

• BSS problem with independent sources, minimize the Kullback-Leibler divergence (D_kl) with deflation and equivariant methods

  

Homework 10

• BSS problem with independent sources, maximize Kurt with fixed-point method (FAST ICA) and another method not sensitive to outliers