In the past several years, there have been exciting breakthroughs in the study of sparse representation of high-dimensional signals. That is, a signal is represented as a linear combination of relatively few base elements in an over-complete dictionary. Much of the excitement centers around the discovery that a sufficiently sparse linear representation can be correctly and efficiently computed by convex optimization (i.e. the L1-L0 equivalence) or greedy algorithms, even though this problem is extremely difficult (NP-hard) in the general case. If this was not surprising enough, further studies have shown that such high-dimensional sparse signals can be accurately recovered from drastically smaller number of (even randomly selected) linear measurements, hence the catch phrase "compressive sensing" or sometimes, "compressed sensing".
These results have already caused a small revolution in the community of statistical signal processing as they provide entirely new perspectives to some of the fundamental principles and doctrines in signal processing such as the sampling bounds and the choice of bases for signal representation and reconstruction. The recent Signal Processing Magazine special issue on Compressive Sampling captures some of the most recent and exciting developments in this field.
We believe that these new results and the general mathematical principles behind them are of great interest to communities far beyond signal processing. The theme of this new special issue for Proceedings of the IEEE is to introduce to the entire electrical engineering community highlights of these new theoretical results, their likely future extensions, and their far-reaching impact on many engineering applications, including but no longer limited to signal processing.
In this special issue, we plan to invite the best experts in each of these areas to contribute an high quality paper. The papers aim to provide excellent exposition of past achievements and highlights in the areas, or feature some new exciting developments by the authors, or discuss promising new directions and extensions. We hope that through the topics and examples featured in this special issue, the readers will be able to grasp the essence of this new method so that they can use it to solve old or new problems in their own field. As the old Chinese proverb goes, our goal is to lay “A Brick to Attract Jade.”
Below are some representative topics: