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:
- Unified framework for localization measures: We shall study systematically existing versions of uncertainty inequalities and localization measures with the aim of developing a unified analytic framework.
- Application oriented localization measures and phase spaces: We shall establish connections between uncertainty principles and the requirements of specific signal/image processing problems, in view of the proposed target applications.
- Optimality concepts for multi waveform systems: Signals with different characteristics are efficiently represented by systems involving more than one elementary waveform. We aim at developing corresponding optimality criteria.