Sampling and Reconstruction: Applications and Advances (10w5122)

Arriving in Banff, Alberta Sunday, November 28 and departing Friday December 3, 2010

Organizers

(University of Florida)

(Simon Fraser University)

(Ecole Polytechnique de Federale Lausanne (EPFL))

Objectives

The goal of our workshop is to bring together researchers from diverse backgrounds (mathematics, signal processing, and computer sciences), who actively research on problems of the representation, reconstruction, analysis, processing, and visualization of multidimensional data. The workshop will focus at the mathematical underpinnings of these subject areas. Largely, we aim at gathering researchers from the established disciplines of signal and image processing, numerical analysis and such application areas as visualization and medical imaging.

In this workshop, we would like to focus on the areas of numerical analysis, digital signal and image processing as well as the area of visualization. We will bring researchers from engineering, computer science and mathematics together to compare the challenges these fields experience and to accelerate the transfer of knowledge across disciplinary boundaries.

We have identified five sub-areas with particular focus topic in each. We have also communicated with internationally recognized experts in each category and confirmed their interest in participating and chairing their focus group.

The objective is to compile a summary of meetings to determine what are the grand challenges in each area and what are the applications that steer theoretical developments.

Multiscale & wavelet analysis. Chair: Ivan Selesnick (Polytechnic University, NY), confirmed.

Sparse sampling, non-uniform sampling and compressed sensing. Chair: Yonina Eldar (Technion, Israel), confirmed.

Reconstruction theory and algorithms, multidimensional signal processing.

Applications, graphics, visualization, medical imaging and fluid
dynamics simulations.

Multiscale and wavelet analysis is an active domain for theoreticians and practitioners. There are about 2000 papers published each year on the subject. The multiscale algorithms are particularly useful when dealing with large datasets as they often allow for efficient algorithms for processing and analysis of data.

Recently, there has been significant endeavour in sparse and non-uniform sampling where the recent trend is to develop methods for sub-Nyquist rate sampling. There are open theoretical questions on the assumptions made on the signal model hence making a specific choice of space suitable for modeling signals with those assumptions. This is a relatively young field with important questions to be answered before we can see its impact on real applications.

Reconstruction and signal processing theory and algorithms deal with processing and analysis and interpolation and approximation of data. Univariate signal processing was mainly developed in the last century to discretize and reconstruct audio signals. Most of the techniques were almost directly applied in the image processing domain in the 60's. However, even from the beginnings of image processing, it was well-known that true multidimensional techniques offer advantages over tensor product univariate signal processing techniques. For instance the use of hexagonal pixels in image processing has been advocated since early times in image processing. This area will include recent advances on optimal sampling lattices and multivariate reconstruction techniques based on splines (i.e., box splines).

Visualization techniques based on simulation of physical phenomena are closely tied with numerical simulation and modeling. This area will cover recent advances on multi-grid and moving mesh methods for solving differential equations as well as optimal sampling lattices employed in fluid flow simulations. This area in our workshop is specifically aimed to prepare a list of recent {bf applications} in neuroscience, biomedical imaging, visualization, image and video processing and various other disciplines that exploit sampling and reconstruction.

Relevance, importance and timeliness of the event

This workshop will be the first of its kind to specifically address the sampling and reconstruction theory and its applications that brings together mathematicians, electrical engineers and computer scientists. This workshop will foster inter-disciplinary work by helping researchers in one field close interaction with researchers in a different field that have common interest in sampling and reconstruction.

This field has progressed recently in each of the sub-areas that were mentioned above. The advances in non-uniform sampling to multivariate reconstruction are deemed to have a strong impact on applications such as digital devices and medical imaging modalities -- to name a few.

We believe that the synergy between mathematicians, engineers and computer scientists in this workshop will accelerate and steer the theoretical developments and will also help translate this research to a wider range of applications in industry.