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.