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.   Optimal localization,
2.   Efficient 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.