French-Austrian bilateral research project funded by the French National Agency of Research (ANR) and the Austrian Science Fund (FWF, project no. I 1362-N30). The project involves two academic partners, namely the Laboratory of Mechanics and Acoustics (LMA - CNRS UPR 7051, France) and the Acoustics Research Institute. At the ARI, two research groups are involved in the project: the Mathematics and Signal Processing in Acoustics and the Psychoacoustics and Experimental Audiology groups.

Principal investigators: Thibaud Necciari (ARI), Piotr Majdak (ARI) and Olivier Derrien (LMA).

Running period: 2014-2017 (project started on March 1, 2014).

One of the greatest challenges in signal processing is to develop efficient signal representations. An efficient representation extracts relevant information and describes it with a minimal amount of data. In the specific context of sound processing, and especially in audio coding, where the goal is to minimize the size of binary data required for storage or transmission, it is desirable that the representation takes into account human auditory perception and allows reconstruction with a controlled amount of perceived distortion. Over the last decades, many psychoacoustical studies investigated auditory masking, an important property of auditory perception. Masking refers to the degradation of the detection threshold of a sound in presence of another sound. The results were used to develop models of either spectral or temporal masking. Attempts were made to simply combine these models to account for time-frequency (t-f) masking effects in perceptual audio codecs. We recently conducted psychoacoustical studies on t-f masking. They revealed the inaccuracy of those models which revealed the inaccuracy of such simple models. These new data on t-f masking represent a crucial basis to account for masking effects in t-f representations of sounds. Although t-f representations are standard tools in audio processing, the development of a t-f representation of audio signals that is mathematically-founded, perception-based, perfectly invertible, and possibly with a minimum amount of redundancy, remains a challenge. POTION thus addresses the following questions:

- To what extent is it possible to obtain a perception-based (i.e., as close as possible to “what we see is what we hear”), perfectly invertible, and possibly minimally redundant t-f representation of sound signals? Such a representation is essential for modeling complex masking interactions in the t-f domain and is expected to improve our understanding of auditory processing of real-world sounds. Moreover, it is of fundamental interest for many audio applications involving sound analysis-synthesis.
- Is it possible to improve current perceptual audio codecs by considering a joint t-f approach? To reduce the size of digital audio files, perceptual audio codecs like MP3 decompose sounds into variable-length time segments, apply a frequency transform, and use masking models to control the sub-quantization of transform coefficients within each segment. Thus, current codecs follow mainly a spectral approach, although temporal masking effects are taken into account in some implementations. By combining an efficient perception-based t-f transform with a joint t-f masking model in an audio codec, we expect to achieve significant performance improvements.

POTION is structured in three main tasks:

- Perception-based t-f representation of audio signals with perfect reconstruction: A linear and perfectly invertible t-f representation will be created by exploiting the recently developed non-stationary Gabor theory as a mathematical background. The transform will be designed so that t-f resolution mimics the t-f analysis properties by the auditory system and possibly no redundancy is introduced to maximize the coding efficiency.
- Development and implementation of a t-f masking model: Based on psychoacoustical data on t-f masking collected by the partners in previous projects and on literature data, a new, complex model of t-f masking will be developed and implemented in the computationally efficient representation built in task 1. Additional psychoacoustical data required for the development of the model, involving frequency, level, and duration effects in masking for either single or multiple maskers will be collected. The resulting signal processing algorithm should represent and re-synthesize only the perceptually relevant components of the signal. It will be calibrated and validated by conducting listening tests with synthetic and real-world sounds.
- Optimization of perceptual audio codecs: This task represents the main application of POTION. It will consist in combining the new efficient representation built in task 1 with the new t-f masking model built in task 2 for implementation in a perceptual audio codec.

More information on the project can be found on the POTION web page.

- 2014): Perceptual matching pursuit with Gabor dictionaries and time-frequency masking, in: Proceedings of the 39th International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014). Florence, Italy, 3126-3130. (proceedings) ICASSP 2014: Perceptual matching pursuit results (

START project of P. Balazs.

This international, multi-disciplinary and team-oriented project will expand the group *Mathematics and Acoustical Signal Processing* at the Acoustic Research Institute in cooperation with *NuHAG* Vienna (Hans G. Feichtinger, M. Dörfler, K. Gröchenig), Institute of Telecommunication Vienna (Franz Hlawatsch), *LATP* Marseille (Bruno Torrésani) *LMA * (Richard Kronland-Martinet). CAHR (Torsten Dau, Peter Soendergaard), the *FYMA* Louvain-la-Neuve (Jean-Pierre Antoine), AG Numerics (Stephan Dahlke), School of Electrical Engineering and Computer Science (Damian Marelli) as well as the BKA Wiesbaden (Timo Becker).

Within the institute the groups Audiological Acoustics and Psychoacoutics, Computational Acoustics, Acoustic Phonetics and Software Development are involved in the project.

This project is funded by the FWF as a START price . It is planned to run from May 2012 to April 2018.

- Kick-off workshop (Vienna, 7.-8.May 2012)
- Mid-term workshop (Marseille, 18.-20-November 2014)
- FLAME Physics workshop (Vienna, 21.-22.Oktober 2015)

We live in the age of information where the analysis, classification, and transmission of information is f essential importance. Signal processing tools and algorithms form the backbone of important technologieslike MP3, digital television, mobile phones and wireless networking. Many signal processing algorithms have been adapted for applications in audio and acoustics, also taking into account theproperties of the human auditory system.

The mathematical concept of frames describes a theoretical background for signal processing. Frames are generalizations of orthonormal bases that give more freedom for the analysis and modificationof information - however, this concept is still not firmly rooted in applied research. The link between the mathematical frame theory, the signal processing algorithms, their implementations andfinally acoustical applications is a very promising, synergetic combination of research in different fields.

Therefore the main goal of this multidisciplinary project is to

*-> Establish Frame Theory as Theoretical Backbone of Acoustical Modeling*

in particular in psychoacoustics, phonetic and computational acoustics as well as audio engineering.

For this auspicious connection of disciplines, FLAME will produce substantial impact on both the heory and applied research.

The theory-based part of FLAME consists of the following topics:

- T1 Frame Analysis and Reconstruction Beyond Classical Approaches
- T2 Frame Multipliers, Extended
- T3 Novel Frame Representation of Operators Motivated by Computational Acoustics

The application-oriented part of FLAME consists of:

- A1 Advanced Frame Methods for Perceptual Sparsity in the Time-Frequency Plane
- A2 Advanced Frame Methods for the Analysis and Classification of Speech
- A3 Advanced Frame Methods for Signal Enhancement and System Estimation

- Wittgenstein und START-Preise 2011
- Interviews auf Ö1
- Zwei START-Preise für ÖAW-Forscher - Mathematiker Peter Balazs und Quantenphysiker Peter Rabl ausgezeichnet
- FWF: Wittgenstein and START-Preis 2011
- START-Preis 2011
- Standard: Schall und Rauschen
- Falter: Heureka

From many previous applications, it is known that inverse problems often require a regularization that makes the inversion numerically stable. In this project, sequences that allow a bounded, injective analysis (that is not boundedly invertible) are investigated, .

Even for general sequences, analysis operator and synthesis operator can be defined. The first part of this project will investigate the most general results of these definitions. For example, it can be shown that the analysis operator is always a closed operator. Although it can be shown that the existence of another sequence that allows a perfect reconstruction fit can not be bounded, the question of how to construct such a "dual sequence" will be investigated.

Such sequences have already found applications in wavelet analysis, in which dual sequences were constructed algorithmically. Also, the original system investigated by Gabor with a redundancy of 1 satisfies this condition.

- M. El-Gebeily, Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Saudi Arabia
- J. P. Antoine, Unité de physique théorique et de physique mathématique – FYMA, Belgium

Funded by the Vienna Science and Technology Fund (WWTF) within the "Mathematics and …2016" Call (MA16-053)

Principal Investigator: Georg Tauböck

Co-Principal Investigator: Peter Balazs

Project Team: Günther Koliander, José Luis Romero

Duration: 01.07.2017 – 01.07.2021

Signal processing is a key technology that forms the backbone of important developments like MP3, digital television, mobile communications, and wireless networking and is thus of exceptional relevance to economy and society in general. The overall goal of the proposed project is to derive highly efficient signal processing algorithms and to tailor them to dedicated applications in acoustics. We will develop methods that are able to exploit structural properties in infinite-dimensional signal spaces, since typically ad hoc restrictions to finite dimensions do not sufficiently preserve physically available structure. The approach adopted in this project is based on a combination of the powerful mathematical methodologies frame theory (FT), compressive sensing (CS), and information theory (IT). In particular, we aim at extending finite-dimensional CS methods to infinite dimensions, while fully maintaining their structure-exploiting power, even if only a finite number of variables are processed. We will pursue three acoustic applications, which will strongly benefit from the devised signal processing techniques, i.e., audio signal restoration, localization of sound sources, and underwater acoustic communications. The project is set up as an interdisciplinary endeavor in order to leverage the interrelations between mathematical foundations, CS, FT, IT, time-frequency representations, wave propagation, transceiver design, the human auditory system, and performance evaluation.

compressive sensing, frame theory, information theory, signal processing, super resolution, phase retrieval, audio, acoustics

Scientific and Technological Cooperation between Austria and Serbia (SRB 01/2018)

Duration of the project: 01.07.2018 - 30.06.2020

Project partners:

Acoustics Research Institute, ÖAW (Austria)

University of Vienna (Austria)

University of Novi Sad (Republic of Serbia)

Project website: http://nuhag.eu/anacres

Scientific and Technological Cooperation with Macedonia 2016-18

Project duration: 01.07.2016 – 30.06.2018

The main aim of the project is to combine the research areas of Frame Theory and Generalized Asymptotic Analysis.

Project partner institutions:

Acoustics Research Institute (ARI), Austrian Academy of Sciences, Vienna, Austria

Ss. Cyril and Methodius University, Skopje, The Former Yugoslav Republic of Macedonia

Project members:

Diana T. Stoeva (Project coordinator Austria), Peter Balazs, Nicki Holighaus, Zdenek Prusa

Katerina Hadzi-Velkova Saneva (Project coordinator FYROM), Sanja Atanasova, Pavel Dimovski, Zoran Hadzi-Velkov, Bojan Prangoski, Biljana Stanoevska-Angelova, Daniel Velinov, Jasmina Veta Buralieva

Project Workshops and Activities:

1) Nov. 24-26, 2016, Ss. Cyril and Methodius University, Skopje

Project Kickoff-workshop

2) Nov. 15-19, 2017, ARI, Vienna

Research on project-related topics

3) April 14-19, 2018, ARI, Vienna

Research on project-related topics

and

ARI-Guest-Talk given at ARI on the 17th of April, 2018: Prof. Zoran Hadzi-Velkov, "*The Emergence of Wireless Powered Communication Networks"*

4) May 25-30, Ss. Cyril and Methodius University, Skopje

Research on project-related topics

and

Workshop "Women in mathematics in the Balkan region" (May 28 - May 29, Ss. Cyril and Methodius University, Skopje)

5) June 14-18, Ss. Cyril and Methodius University, Skopje

Research on project-related topics

and

Summer course "An Introduction to Frame Theory and the Large Time/Frequency Analysis Toolbox" (June 14-15), Lecturers: Diana Stoeva and Zdenek Prusa (from ARI)

6) Mini-Symposium "Frame Theory and Asymptotic Analysis" organized at the European Women in Mathematics General Meeting 2018, Karl-Franzens-Universität Graz, Austria, 3-7 September 2018.

7) November 17-20, 2018, ARI, Vienna

Work on project-related topics

Multilateral Scientific and Technological Cooperation in the Danube Region 2017-2018

Austria, Czech Republic, Republic of Serbia, and Slovak Republic

Project duration: 01.01.2017 - 31.12.2018

Project website: nuhag.eu/tifmofus

Numerous implementations and algorithms for time frequency analysis can be found in literature or on the internet. Most of them are either not well documented or no longer maintained. P. Soendergaard started to develop the Linear Time Frequency Toolbox for MATLAB. It is the goal of this project to find typical applications of this toolbox in acoustic applications, as well as incorporate successful, not-yet-implemented algorithms in ST^{x}.

The linear time-frequency toolbox is a small open-source Matlab toolbox with functions for working with Gabor frames for finite sequences. It includes 1D Discrete Gabor Transform (sampled STFT) with inverse. It works with full-length windows and short windows. It computes the canonical dual and canonical tight windows.

These algorithms are used for acoustic applications, like formants, data compression, or de-noising. These implementations are compared to the ones in STx, and will be implemented in this software package if they improve its performance.

- H. G. Feichtinger et al., NuHAG, Faculty of Mathematics, University of Vienna
- B. Torrèsani, Groupe de Traitement du Signal, Laboratoire d'Analyse Topologie et Probabilités, LATP/ CMI, Université de Provence, Marseille
- P. Soendergaard, Department of Mathematics, Technical University of Denmark

General frame theory can be more specialized if a structure is imposed on the elements of the frame in question. One possible, very natural structure is sequences of shifts of the same function. In this project, irregular shifts are investigated.

In this project, the connection to irregular Gabor multipliers will be explored. Using the Kohn Nirenberg correspondence, the space spanned by Gabor multipliers is just a space spanned by translates. Furthermore, the special connection of the Gramian function and the Grame matrix for this case will be investigated.

A typical example of frames of translates is filter banks, which have constant shapes. For example, the phase vocoder corresponds to a filter bank with regular shifts. Introducing an irregular shift gives rise to a generalization of this analysis / synthesis system.

- S. Heineken, Research Group on Real and Harmonic Analysis, University of Buenos Aires

For many important applications - like virtual reality, communication, sound design, audio compression & coding, and hearing aids - a mathematical representation that matches or approximates the perception of the human auditory system is needed. For solving this critical and prominent problem, a trans-disciplinary approach is necessary. The goals of this project are:

- design, development and evaluation of new representations of audio signals,
- development of new tools based on the mathematic theory of time-frequency (or time-scale) representations (Gabor, wavelet or other),
- development of the mathematic background for applications in audio perception and psychoacoustics,
- and evaluation of these representations with auditory and psychoacoustic tests.

- R. Kronland-Martinet, S. Ystad, T. Necciari, Modélisation, Synthèse et Contrôle des Signaux Sonores et Musicaux of the LMA / CRNS Marseille
- S. Meunier, S. Savel, Acoustique perceptive et qualité de l’environnement sonore of the LMA / CRNS Marseille

This is a partner project of the ANR project senSons.

During the current project of efficiently calculating a resynthesis window and an iterative scheme for a finite element method algorithm for vibrations in soils and liquids, it became apparent that block matrices are a powerful tool to find numerically efficient algorithms.

In this project, the focus should be the investigation of the numeric features of block matrices. How can this structure be used to calculate or approximate the inverse of a matrix or its norm? How can this be used to speed up iterative schemes?

The results will be used for the two projects mentioned below:

- double preconditioning for Gabor frames
- vibrations in random layers