Positive Reviews for the finalized FLAME project

The Acoustics Research Institute (ARI) has successfully finalized its multidisciplinary project “Frames and Linear Operators for Acoustical Modeling and Parameter Estimation (FLAME)”. It was funded by the renowned START program of the FWF. The project ran for eight years until 2020. Recently, the posthoc reviews for the full project and final report presented a very positive impression of the project.

 

One of the applications of the frame theory concerns the optimization of resynthesis of time-frequency representations. Windows are used to cut out signal part´s to allow a localized frequency transformation. In FLAME we have created a method for designing windows, that allow perfect resynthesis, but have different properties than the usual “dual” window. The first column shows the time representation, the second the frequency representation and the third the time-frequency representation of the windows. It is easy to see how different the windows are, although both allow perfect resynthesis.
In: N. Perraudin, N. Holighaus, P. Soendergaard, P. Balazs, "Designing Gabor windows using convex optimization", Applied Mathematics and Computation, Vol. 330, pp. 266-287 (2018), preprint on arxiv

The overall ambitious goal of the project was to establish abstract frame theory as theoretical backbone of acoustical modeling in particular in psychoacoustics, phonetics and computational acoustics as well as audio engineering. The project FLAME managed to fulfill this goal by providing significant results both for the applied sciences and for theoretical mathematics.

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 modification of information than other methods.

The reviews for the final report came back very positive commenting that „this project is inherently interdisciplinary”, and that “the project has seen many of the participants rise to worldwide recognition.” “The scientific success is very strong. The  project produced 98 publications, many of which were published in top journals …. The importance for related disciplines is illustrated by the many publications in top journals in physics and engineering.”

Publications

  • Phase-Based Signal Representations for Scattering. / Haider, D; Holighaus, N; Balazs, P.
    European Signal Processing Conference (EUSIPCO21). 2021.
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  • A survey on the unconditional convergence and the invertibility of multipliers with implementation. / Stoeva, D. T.; Balazs, P.; Casey, S. D. (Editor) et al.
    Sampling - Theory and Applications. Applied and Numerical Harmonic Analysis. Cham: Unknown Publisher, 2020. p. 169 - 192.
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  • On a characterization of Riesz bases via biorthogonal sequences. / Stoeva, D. T.
    In: Journal of Fourier Analysis and Applications, Vol. 26, 01.12.2020, p. 67.
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  • Frame expansions of test functions, tempered distributions, and ultradistributions. / Pilipović, S.; Stoeva, D. T.; Lindahl, K. (Editor) et al.
    Analysis, Probability, Applications, and Computation. Trends in Mathematics. Birkhäuser, Cham, 2019. p. 455 - 463.
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  • Computing reconstructions from nonuniform Fourier samples: Universality of stability barriers and stable sampling rates. / Adcock, B.; Gataric, M.; Romero, J.L.
    In: Applied and Computational Harmonic Analysis, Vol. 46, 01.12.2019, p. 226-249.
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  • Frames for the solution of operator in Hilbert spaces with fixed dual pairing. / Balazs, P.; Harbrecht, H.
    In: Numerical Functional Analysis and Optimization, Vol. 40, 01.12.2019, p. 65-84.
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  • An Operator Based Approach to Irregular Frames of Translates. / Balazs, P.; Heineken, S.
    In: Mathematics as part of the Special Issue Harmonic Analysis, 01.12.2019.
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  • U-cross Gram matrices and their invertibility. / Balazs, P.; Shamsabadi, M.; Arefijamaal, A. et al.
    In: Journal of Mathematical Analysis and Applications, Vol. 476, 01.12.2019, p. 367-390.
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  • Kernel Theorems in Coorbit Theory. / Balazs, P.; Gröchenig, K.; Speckbacher, M.
    In: Transactions of the American Mathematical Society, 01.12.2019.
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  • Adhoc method to Invert the Reassigned Time-Frequency Representation. / Rajbamshi, S.; Balazs, P.; Holighaus, N.
    Proceedings of the 23rd International Congress on Acoustics. 2019. p. 2789 - 2796.
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  • Random Gabor Multipliers for Compressive Sensing: A Simulation Study. / Rajbamshi, S; Tauböck, G; Balazs, P et al.
    Proceedings of the EUSIPCO 2019. 2019.
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  • Harmonic-aligned Frame Mask Based on Non-stationary Gabor Transform with Application to Content-dependent Speaker Comparison. / Huang, F.; Balazs, P.
    Interspeech 2019. 2019.
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  • Extraction of Rhythmical Features with the Gabor Scattering Transform. / Haider, D.; Balazs, P.
    Proceedings of the 14th International Symposium on Computer Music Multidisciplinary Research (CMMR), Marseille, France, Oct. 14-18. 2019. p. 916-923.
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  • Continuous warped time-frequency representations - Coorbit spaces and discretization. / Holighaus, N.; Wiesmeyr, C.; Balazs, P.
    In: Applied and Computational Harmonic Analysis, Vol. 47/3, 20.08.2019, p. 975-1013.
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  • Frame Multipliers - a mathematical background for time-variant filters and auditory scene analysis. / Balazs, P.
    Fortschritte in der Akustik (DAGA 2018). 2018.
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  • Designing Gabor windows using convex optimization. / Perraudin, N.; Holighaus, N.; Sondergaard, P. L. et al.
    In: Applied and Computational Mathematics, Vol. 330, 01.12.2018, p. 266 - 287.
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  • Audlet Filter Banks: A Versatile Analysis/Synthesis Framework using Auditory Frequency Scales. / Necciari, T; Holighaus, N; Balazs, P. et al.
    In: Applied Sciences (Switzerland), Vol. 8, 01.12.2018, p. 96-117.
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  • Inpainting of Long Audio Segments with Similarity Graphs. / Perraudin, N.; Holighaus, N.; Majdak, P. et al.
    In: IEEE/ACM Transactions on Audio, Speech, and Language Processing, Vol. 26, 01.12.2018, p. 1079-1090.
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  • Operator representations of sequences and dynamical sampling. / Christensen, O.; Hasannasab, M.; Stoeva, D. T.
    In: Default journal, Vol. 17, 01.12.2018, p. 29-42.
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  • Dictionary learning for pitch estimation in speech signals. / Huang, F.; Balazs, P.
    2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP). 2017. p. 1-6.
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