The goal is the development of efficient algorithms for signal decomposition and processing exploiting the mathematical tools developed in the work packages Localization Measures, Construction of Minimizers and Frames and Signal Expansions. We shall develop, analyse, implement and test algorithms for computing the transforms associated to waveform systems, for obtaining optimal signal expansions with respect to these systems, and for solving standard benchmark problems. A main objective is to come out with algorithms and implementations that outperform state of the art methods for these benchmark test problems. Another main goal is to provide efficient and portable implementations, that will be made available to all groups of the consortium for testing, in particular in view of GPU Implementation and 3D MALDI Imaging developments.
We have the following aims:
- Transform / Synthesis: The frames and dictionaries constructed in UNLocX form the building blocks for efficient representations of data. But putting them to use requires efficient algorithms to compute analysis coefficients and, similarly, to reconstruct or approximate signals from coefficients. In particular we will focus on algorithms devoted to signals and images leveraging the structure and invariance properties provided by phase-space discretizations to perform fast computations (for example FFT- or DWT-based).
- Coding and sparsity concepts: The representations systems developed in UNLocX will be particularly suited to generate sparse representation thanks to optimal localization properties. We aim at leveraging the expected sparsity of localized frames provided in UNLocX for coding, de-noising and restoration purposes.
- Bechmark test: To provide a comprehensive means of testing the algorithms developed in UNLocX we propose to build an evaluation and testing framework.