#
Frames for the finite world: Sampling, coding and quantization

August 18 to August 22, 2008
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Sinan Gunturk,
Goetz Pfander,
Holger Rauhut,
and Ozgur Yilmaz

## Original Announcement

This workshop will be devoted to frame theory in finite dimensions with an emphasis
on compressive sensing and quantization theory for frames.
Recent years have seen significant advances in a number of subjects in
signal processing and information theory in which frame theory
has played a central role. Some of the most important of these
"finite world" applications are
analog-to-digital (A/D) conversion, coding theory, and compressive sensing.
While these subjects fit well within electrical engineering, several
key contributions have been made by mathematicians who have strong
interest in real-world applications, resulting in fruitful
interdisciplinary research collaborations.

A frame is a collection of vectors in a Hilbert space
allowing for a stable linear decomposition of
any element in the space, similar to a basis expansion.
However, a frame is not required to be linearly independent,
and consequently, expansion coefficients can be highly non-unique.
This redundancy
is advantageous for applications in which additional constraints
need to be imposed, such as the set of coefficients being sparse or
quantized. The nature of such constraints also establishes a venue for
the design of specific frames. This workshop will be concerned with
the construction, properties, and applications
of frames in finite dimensions.

The workshop will focus on the following specific topics:

- Construction of good deterministic frames (measurement matrices) for
compressive sensing.
- Quantization theory for frames: rate-distortion theory, coarse quantization, redundancy vs. robustness, A/D conversion with compressive sensing.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.