Algorithms in signal and image processing have reached an impressive level of sophistication and computing power still increases at an exponential rate. However, high-tech applications have an ever-increasing demand for even more efficient algorithms, even more powerful computers and new concepts for advancing applications.Starting from a recently discovered gap in the theory of uncertainty principles, this project aims at developing a framework for constructing problem adapted, ultra-efficient algorithms concerning (de-)coding and analyzing/synthesizing signals/images. We expect, that this will allow us to tackle complex applications in life sciences and ultra precise audio signal processing which presently cannot be solved appropriately with existing algorithms on existing computers.The key for developing these algorithms is a representation of signals and images by function systems, which satisfy the following requirements:1.\tOptimal localization,2.\tEfficient discretization.The theoretical foundation of this approach is based on the definition of suitable localization measures in generalized phase spaces and the construction of minimizing waveforms. These waveforms are then the basic building blocks in discretization schemes.We expect that this approach allows us to shift the limits of the efficiency vs. precision paradigm considerably. The efficiency of an abstract algorithm has to be evaluated in connection with the computer hardware (parallelization, data exchange, storage) used. Accordingly, our proof of principle includes implementations of baseline algorithms as well as of advanced GPU implementations.As final proof of principle we apply these methods for two challenging applications in audio signal design and life sciences (proteomics). The evaluation will be done by our industrial consortium partners together with our advisory board consisting of one SME, one world market leader and two internationally highly recognized scientific experts.