Localization Measures

The goal is to develop a systematic theory for uncertainty principles in generic phase spaces, in view of signal/image/data processing applications. We will study existing formulations (Heisenberg type inequalities, entropy inequalities, ambiguity function formulations) and develop a unified framework for uncertainty bounds and corresponding optimal waveforms. We will also study uncertainty principles in the context of specific signal processing tasks (e.g. signal coding and signal analysis/understanding) and derive corresponding task-oriented versions of inequalities.

The aims are as follows: