Pré-Publication, Document De Travail Année : 2021

Generalized SU(1,1) Equivariant Convolution on Fock-Bargmann Spaces for Robust Radar Doppler Signal Classification

Frédéric Barbaresco

Résumé

Classifying radar Doppler signals with Deep Learning algorithms is a challenging task, in particular because of the noisy nature of the data (clutter, thermal noise, etc.). Equivariant Neural Networks (ENN) have already been shown very promising in this context by coupling hyperbolic embedding techniques with dedicated SU(1,1) convolution operators in order to achieve local robustness by-design. In this paper, we introduce a generalized SU(1,1) equivariant convolution operator on the Fock-Bargmann spaces by leveraging on the representations of SU(1,1) over these functional Hilbert spaces. We further give a new way of sampling over SU(1,1) for Monte-Carlo computations by using a generalization of the Bloch-Messiah decomposition of elements of the symplectic group SL(2,R) to those of SU(1,1). We finally illustrate our approach on the problem of radar clutter classification and demonstrate in this context that SU(1, 1) ENN achive better performance results than conventional approaches from both accuracy and robustness standpoints.
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Dates et versions

hal-03309817 , version 1 (30-07-2021)

Identifiants

  • HAL Id : hal-03309817 , version 1

Citer

Pierre-Yves Lagrave, Frédéric Barbaresco. Generalized SU(1,1) Equivariant Convolution on Fock-Bargmann Spaces for Robust Radar Doppler Signal Classification. 2021. ⟨hal-03309817⟩
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