### Welcome to FrameLab.org!

Frames are systems that provide robust, stable and usually
non-unique representations of vectors. They have been a focus of
research in the last two decades in applications where redundancy
plays a vital and useful role, e.g., filter bank theory, sigma-delta
quantization, image processing, and wireless communications.

Frames provide us with an expansion of all vectors in terms of
"elementary building blocks", in much the same way as basis do, and
hereby helps us reducing many questions concerning general vectors to
similar questions concerning only the basis elements. A frame for a
vector space also allows each vector in the space to be written as a
linear combination of the elements in the frame, but linear
independence between the frame elements is not required. Readers new to
the notion of frames can, intuitively, think of a frame as a basis
to which one has added more elements.

However, a number of new applications have emerged where the set-up can hardly be modeled
naturally by one single frame system. They generally share a common property that requires
distributed processing such as sensor networks. In this
case it would be highly beneficial to split a large frame system into a set of (overlapping)
much smaller systems, and being able to process effectively locally within each sub-system.
This led to the development of a suitable theory based on fusion frames, which provides exactly
the framework not only to model these applications but also to provide efficient algorithms
with sufficient robustness. It can be shown that fusion frames contain conventional frames as a very special
case, thereby going beyond frame theory.

Although frame and also fusion frames are by now a standard method for data processing, no software package combining algorithms for
all essential frame (and fusion frame)-related procedures has been available so far. Such procedures can be either constructions and
implementations of analyzing properties of frames and fusion frames, or algorithms for data processing with frames and fusion frames. With
the material provided on this webpage, we
intend to close this gap.

Our ultimate goal with this webpage is public release of an extensive software package for frame (and fusion frame)-related algorithms.

*We invite you explore this website, which
provides you with information about frames and their applications,
publications about these topics, downloadable software, and much more!
We also welcome any comment
or suggestion!*

© Gitta Kutyniok 2010