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Fast algorithm for determined blind source separation with update of demixing filters with joint adjustment of the remaining sources.

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AuxIVA with Iterative Projection with Adjustment Updates

This repository contains the code for the paper "Independent Vector Analysis via Log-Quadratically Penalized Quadratic Minimization" by Robin Scheibler.

Abstract

We propose a new algorithm for blind source separation (BSS) using independent vector analysis (IVA). This is an improvement over the popular auxiliary function based IVA (AuxIVA) with iterative projection (IP) or iterative source steering (ISS). We introduce iterative projection with adjustment (IPA), where we update one demixing filter and jointly adjust all the other sources along its current direction. Each update involves solving a non-convex minimization problem that we term log-quadratically penalized quadratic minimization (LQPQM), that we think is of interest beyond this work. In the general case, we show that its global minimum corresponds to the largest root of a univariate function, reminiscent of modified eigenvalue problems. We propose a simple procedure based on Newton-Raphson to efficiently compute it. Numerical experiments demonstrate the effectiveness of the proposed method. First, we show that it efficiently decreases the value of the surrogate function. In further experiments on synthetic mixtures, we study the probability of finding the true demixing matrix and convergence speed. We show that the proposed method combines high success rate and fast convergence. Finally, we validate the performance on a reverberant blind speech separation task. We find that all the AuxIVA-based methods perform similarly in terms of acoustic BSS metrics. However, AuxIVA-IPA converges faster. We measure up to 8.5 times speed-up in terms of runtime compared to the next best AuxIVA-based method, depending on the number of channels and the signal-to-noise ratio (SNR).

Author

Summary of Experiments

Solve Random SeDJoCo Problems

Evaluate the performance of the proposed method to minimize the surrogate function only.

Separation of Synthetic Mixtures

Evaluate many IVA algorithms for the separation of data following the spherical Laplace distribution.

Separation of Reverberant Speech Mixtures

Evaluate the performance of many IVA algorithms for the separation of reverberant speech.

Test Run the Algorithms

The example.py program allows to test the different algorithms on simulated scenarios. For example, try running

python ./example.py -a auxiva-ipa -m 4

to separate four sources with four microphones using the algorithm overiva-ip2. The full usage instructions is provided below.

> python ./example.py --help
usage: example.py [-h] [--no_cb]
                  [-a {auxiva,auxiva2,auxiva-iss,overiva,overiva-ip,overiva-ip2,overiva-ip-block,overiva-ip2-block,overiva-demix-bg,five,ogive,ogive-mix,ogive-demix,ogive-switch,auxiva-pca,auxiva-ipa,pca}]
                  [-d {laplace,gauss}] [-i {pca}] [-m MICS] [-s SRCS]
                  [-z INTERF] [--sinr SINR] [-n N_ITER] [--gui] [--save]
                  [--seed SEED]

Demonstration of blind source extraction using FIVE.

optional arguments:
  -h, --help            show this help message and exit
  --no_cb               Removes callback function
  -a {auxiva,auxiva2,auxiva-iss,overiva,overiva-ip,overiva-ip2,overiva-ip-blok,overiva-ip2-block,overiva-demix-bg,five,ogive,ogive-mix,ogive-demix,ogive-switch,auxiva-pca,auxiva-ipa,pca}, --algo {auxiva,auxiva2,auxiva-iss,overiva,overiva-ip,overiva-ip2,overiva-ip-block,overiva-ip2-block,overiva-demix-bg,five,ogive,ogive-mix,ogive-demix,ogive-switch,auxiva-pca,auxiva-ipa,pca}
                        Chooses BSS method to run
  -d {laplace,gauss}, --dist {laplace,gauss}
                        IVA model distribution
  -i {pca}, --init {pca}
                        Initialization, eye: identity, eig: principal
                        eigenvectors
  -m MICS, --mics MICS  Number of mics
  -s SRCS, --srcs SRCS  Number of sources
  -z INTERF, --interf INTERF
                        Number of interferers
  --sinr SINR           Signal-to-interference-and-noise ratio
  -n N_ITER, --n_iter N_ITER
                        Number of iterations
  --gui                 Creates a small GUI for easy playback of the sound
                        samples
  --save                Saves the output of the separation to wav files
  --seed SEED           Random number generator seedc

Reproduce the Results

The script prepare_figures.sh was used to prepare the figures of the paper. If the simulations are re-run, it should be edited to adjust the result file names.

Random SeDJoCo Problems

    # Run the simulation, creates <result_file> in `data/` folder
    python ./experiment_head.py
    
    # Create the figure
    python ./experiment_head_plot.py data/<result_file>

Separation of Synthetic Mixtures

    # Run the simulation, creates <result_file> in `data/` folder
    python ./experiment_iva.py
    
    # Create the figure
    python ./experiment_iva_plot.py data/<result_file>

Separation of Reverberant Speech Mixtures

The code can be run serially, or using multiple parallel workers via ipyparallel. Moreover, it is possible to only run a few loops to test whether the code is running or not.

  1. Run test loops serially

     python ./paper_simulation.py ./experiment_ipa_config.json -t -s
    
  2. Run test loops in parallel

     # start workers in the background
     # N is the number of parallel process, often "# threads - 1"
     ipcluster start --daemonize -n N
    
     # run the simulation
     python ./paper_simulation.py ./experiment_ipa_config.json -t
    
     # stop the workers
     ipcluster stop
    
  3. Run the whole simulation

     # start workers in the background
     # N is the number of parallel process, often "# threads - 1"
     ipcluster start --daemonize -n N
    
     # run the simulation
     python ./paper_simulation.py ./experiment_ipa_config.json
    
     # stop the workers
     ipcluster stop
    

The results are saved in a new folder data/<data>-<time>_speed_contest_journal_ipa_<flag_or_hash> containing the following files

parameters.json  # the list of global parameters of the simulation
arguments.json  # the list of all combinations of arguments simulated
data.json  # the results of the simulation

The figures and tables can be produced as follows.

# figure with box-plots of SDR/SIR
python ./make_figure3_journal_ipa_separation_hist.py \
  ./data/<result_folder>/ --pca

# figure with wall-clock vs SDR/SIR
python ./make_figure4_journal_ip_speed_contest.py \
  ./data/<result_folder>/ --pca --pickle

# runtime table
python ./make_table_runtime.py data/<result_folder>/ --pickle

License

The code is provided under MIT license.

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