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 of convolutive mixtures using independent vector analysis. This is an improvement over the popular auxiliary function based independent vector analysis (AuxIVA) with iterative projection (IP) or iterative source steering (ISS). We introduce iterative projection with adjustment (IPA), whereas we update one demixing filter and jointly adjust all the other sources along its current direction. We implement this scheme as multiplicative updates by a rank-2 perturbation of the identity matrix. 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. We find that the global minimum of an LQPQM can be efficiently computed. In the general case, we show that all its stationary points can be characterized as zeros of a kind of secular equation, reminiscent of modified eigenvalue problems. We further prove that the global minimum corresponds to the largest of these zeros. We propose a simple procedure based on Newton-Raphson seeded with a good initial point to efficiently compute it. We validate the performance of the proposed method for blind acoustic source separation via numerical experiments with reverberant speech mixtures. We show that not only is the convergence speed faster in terms of iterations, but each update is also computationally cheaper. Notably, for four and five sources, AuxIVA with IPA converges more than twice as fast as competing methods.

Author

• Robin Scheibler

Summary of Experiments

Experiment 1: Separation performance

Separation performance for different numbers of sources and microphones.

Experiment 2: Speed contest

Plot iterations/runtime of algorithm vs SIR.

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 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

Figure 1., 2., 3., and 4. from the paper are produced then by running

./prepare_figures.sh

License

The code is provided under MIT license.