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Enhanced Matching Pursuit Implementation (empi)
Author: Piotr Różański ⓒ 2015–2018
& improvements of code and build process thanks to Aleks Chrabrow

What is empi?

empi is an implementation of Matching Pursuit algorithm (Mallat, Zhang 1993) with optimal Gabor dictionaries (Kuś, Różański, Durka 2013). It is a highly-optimized multithreaded version written in C++, designed as a faster replacement for MP5. Therefore, it shares most of the input/output specification with MP5, and can be used as MP decomposition tool in SVAROG.

The goal is an optimal decomposition of the input signal as a linear combination of functions from predefined set (dictionary) of Gabor atoms, including ordinary Gaussians as a special case for frequency = 0.

How to get empi?

You can compile empi from source, or download the precompiled versions from the “Releases” tab. Both are available on project's GitHub. If you decide to use the precompiled binaries, you can skip the “Compilation” section altogether. However, since the purpose of the provided binaries is to be as compatible as possible, they may not take full advantage of your specific architecture. To achieve maximal performance, compiling empi from source is recommended.

Additionally, precompiled binaries for OS X does not support OpenMP (therefore, they run a single thread). To use OpenMP on OS X, compilation is necessary.



To compile empi, CMake build system is required. The only external library requirement is the FFTW library in version 3. Both library and the development headers must be installed to compile empi. Under Ubuntu, package “libfftw3-dev” does the trick. MacOS and other Linux distributions may have packages of slightly different names. Under Windows, follow the FFTW installation instructions.

Also, you will need a modern C++ compiler with support for C++11 standard. OpenMP support is recommended. Under OS X, OpenMP runtime (available at LLVM Download Page) should be downloaded and put into system library directory (e.g. /usr/lib) prior to compiling.


This project uses CMake, so the proper way of compilation depends on your environment. Generally speaking, you can use CMake-gui to generate build files for your specific configuration.

Unix-family OS

The easiest way is to run

cmake .

or, if you need to build standalone binaries (however, it will disable some platform-specific optimizations),

cmake -DSTANDALONE=1 .

followed by


in the directory where you cloned your repository; you can also do an out-of-source build, if you prefer. If successful, binary file “empi” shall appear. It can by installed to system directory (e.g. /usr/local/bin) by calling

sudo make install


Binaries can also be cross-compiled for a different system or architecture. Detailed information on cross-compiling empi can be found in the Appendix, at the end of this document.

How to use empi?

Single invocation of empi will

  • read a single binary file (or its part),
  • decompose it as a linear combination of Gabor atoms, and
  • save the results to a specified format (currently only SVAROG's “book” format is supported).

empi needs to be run with a single command-line argument: a path to the configuration file. If run with no arguments, it will print the correct usage. For backward compatibility with MP5, all arguments starting with “-” are ignored.

Configuration file format

Let us start with a sample configuration file:

energyError 0.01
maximalNumberOfIterations 50
energyPercent 99.0


nameOfDataFile signal.bin
nameOfOutputDirectory .
samplingFrequency 128.0

numberOfChannels 3
selectedChannels 1-3

numberOfSamplesInEpoch 1280
selectedEpochs 1-2

Most parameters are straightforward, but we shall describe them one by one:

  • energyError is the ε² parameter in optimal Gabor dictionary construction. Usually the values will be close to 0. Smaller value will allow for a more precise decomposition, but it will also engage more time and RAM.

  • maximalNumberOfIterations is the upper limit for the number of iterations, and therefore, a maximal number of atoms in the resulting decomposition.

  • energyPercent is the percent of the energy that we require to be “explained” by decomposition, Requiring 99% of energy to be explained means that we will be performing decomposition until residual energy fall below 1% of the total energy of the signal.

The decomposition will iterate until maximalNumberOfIterations or energyPercent will be fulfilled, whichever comes first.

  • MP is a selected variant of Matching Pursuit. Following variants are supported:

    • “SMP” decomposes every channel independently

    • “MMP1” finds, in every iteration, set of atoms which differ only in amplitude, optimizing sum of squares of the scalar products across channels

    • “MMP2” finds, in every iteration, set of atoms which differ only in amplitude, optimizing sum of the scalar products across channels (much faster than MMP1)

    • “MMP3” finds, in every iteration, set of atoms which differ in amplitude and/or phase, optimizing sum of squares of the scalar products across channels

  • nameOfDataFile is a path to the binary signal file, relative to the current directory. The input file should consist of 32-bit float values in the byte order of the current machine (no byte-order conversion is performed). For multichannel signals, first come the samples for all channels at t=0, then for all channels at t=Δt, and so forth. In other words, the signal should be written in column-major order (rows = channels, columns = samples).

  • nameOfOutputDirectory is a path to the output directory, relative to the current directory. The output file will be named based on the name of the input file, e.g. if input file is “signal.bin”, the output will be named “signal_XYZ.b”, where XYZ is the selected variant of MP (parametr MP).

  • samplingFrequency is a sampling frequency of the input signal, specified in hertz.

  • numberOfChannels is a number of all channels in the input signal.

  • selectedChannels specify which channels should be read from the signal and decomposed. These can be specified as a single channel 1, as an interval 1-5, as a list 3,4 or mixed: 1-2,5,8-10.

  • numberOfSamplesInEpoch specifies the size of each signal segment (in samples); segments will be processed in order, and their decomposition will be written to the same output file. This parameter is optional; if not given, the entire signal will be processed as a single segment.

  • selectedEpochs is only valid with numberOfSamplesInEpoch and it specifies a list of epoch numbers (starting from 1) to be processed. These can be passed as a single epoch 1, as an interval 1-100, as a list 1,2,3 or mixed: 1-100,201-300,400. This parameter is optional; if not given, then all epochs (the entire signal) will be processed.

  • minAtomScale specifies the minimum scale of atoms in the MP dictionary. If not specified, it defaults to the scale length of 2 samples (scale in seconds = 2 / sampling frequency)

  • maxAtomScale specifies the maximum scale of atoms in the MP dictionary. If not specified, it defaults to the length of the analysed signal.

  • maxAtomFrequency specifies the maximum frequency (in hertz) of atoms in the MP dictionary.

Specifying minAtomScale, maxAtomScale and maxAtomFrequency is not mandatory, but it allows to greatly reduce the computational time.


empi is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

empi is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with empi (file “LICENCE”); if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

Appendix. Cross-compiling empi

This section is dedicated to the steps needed to cross-compile empi for a different operating system and/or architecture on 64-bit Linux (specifically Ubuntu 15.10).

32-bit Linux

Package g++-multilib and libc6-dev-i386 must be installed. Also, static version of FFTW library must be cross-compiled for 32-bit system and available in the toolchain. To cross-compile FFTW, simply pass C_FLAGS=-m32 to the library's ./configure script. Having it all set, return to the empi directory, run

make empi-lin32

and that's it.

Apple Mac (OS X)

This is probably the most complex case. The project osxcross is a good start. It allows to build a full cross-compiling toolchain for both 32-bit and 64-bit OS X compilation. This section will focus on 64-bit toolchain (32-bit is analogous). As a part of its configuration, it is necessary to sign up for the Apple developer's account and download the Xcode package from the official Apple site (don't worry, it's free).

After the toolchain is built, it is necessary to build the FFTW library and copy it (the library itself and header files) into the toolchain. To successfully compile FFTW, it is necessary to specify all the paths to the compiler binaries, e.g. (some of the below may not be necessary)

AR=x86_64-apple-darwin15-ar \
AS=x86_64-apple-darwin15-as \
CC=x86_64-apple-darwin15-clang \
LD=x86_64-apple-darwin15-ld \
RANLIB=x86_64-apple-darwin15-ranlib \
./configure --host=x86_64-apple

The static version of compiled FFTW library (libfftw3.a) has to be placed in the toolchain library directory.

Having it all set, return to the empi directory, run

make empi-osx64

and that's it, finally. The cross-compiled version will not use OpenMP.

Microsoft Windows

Both 32-bit or 64-bit Windows binaries can be cross-compiled. Packages g++-mingw-w64-i686 (for 32-bit) and g++-mingw-w64-x86-64 (for 64-bit) must be installed. Since FFTW developers generally discourage manually compiling FFTW for Windows, it is better to stick with shared versions, which can be obtained from FFTW download page. After downloading, install DLL files and include headers in each toolchain (i686 and/or x86-64), e.g.:

  • /usr/lib/gcc/i686-w64-mingw32/5.3-win32 for 32-bit Windows
  • /usr/lib/gcc/x86_64-w64-mingw32/5.3-win32 for 64-bit Windows

To generate cross-compiled exe files, execute

make empi-win32.exe empi-win64.exe

To use generated binaries under MS Windows, the dynamic version of FFTW library (DLL file) has to be placed in the same directory as the executable file. All the other libraries will be linked statically into the executable.

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