Five ways to recover the symbol of a non-binary localization operator

Abstract

Five constructive methods for recovering the symbol of a time-frequency localization operator with non-binary symbol are presented, two based on earlier work and three novel methods. For the two derivative methods which have previously been applied to binary symbols, we propose a changed symbol estimator and provide additional estimates that show how we can recover non-binary symbols. The three novel methods each have their own advantages and are all applicable to non-binary symbols. Two of them rely on prescribing the input of the localization operator and examining the output, allowing for targeting of the part of the symbol one wishes to recover while the last one relies on spectral information about the operator. All five methods are also implemented numerically and evaluated with the code available.

arXiv comment28 pages, 9 figures

References in corpus (5)

• An Inverse Problem for Localization Operators
• Correspondence theory on $p$-Fock spaces with applications to Toeplitz algebras
• Signal Analysis via the Stochastic Geometry of Spectrogram Level Sets
• Zeros of Gaussian Weyl-Heisenberg functions and hyperuniformity of charge
• Measure-operator convolutions and applications to mixed-state Gabor multipliers