This repository contains the code for the paper "Independent Vector Analysis via Log-Quadratically Penalized Quadratic Minimization" by Robin Scheibler.
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).
Evaluate the performance of the proposed method to minimize the surrogate function only.
Evaluate many IVA algorithms for the separation of data following the spherical Laplace distribution.
Evaluate the performance of many IVA algorithms for the separation of reverberant speech.
The example.py program allows to test the different algorithms on simulated scenarios.
For example, try running
python ./example.py -a auxiva-ipa -m 4to 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 seedcThe 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.
# Run the simulation, creates <result_file> in `data/` folder
python ./experiment_head.py
# Create the figure
python ./experiment_head_plot.py data/<result_file> # Run the simulation, creates <result_file> in `data/` folder
python ./experiment_iva.py
# Create the figure
python ./experiment_iva_plot.py data/<result_file>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.
Run test loops serially
python ./paper_simulation.py ./experiment_ipa_config.json -t -sRun 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 stopRun 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 stopThe 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 simulationThe 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>/ --pickleThe code is provided under MIT license.