Amazing discoveries.

Sometimes you read a series of paper and you know that there is something big behind it. Here are two examples:

The first one is by Emmanuel Candes and Dave Donoho: A Surprisingly Effective Nonadaptive Representation for Objects with Edges. As Bruno Olshausen has shown, most natural images seem to be made of edges and the human eye seem to be good a detecting those. What this article says is that there is no need for our eye system to be adaptive to figure out an image. This is an impressive result because most people think otherwise.

The second series of papers by Emmanuel Candes, Justin Romberg and Terence Tao entitled Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information and Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? show that the right type of signal, decomposed with the right bases, can be reconstructed using an simple linear optimization algorithm. This finding is tied to ubiquitous power laws.