I finished reading, from cover to cover, the March 2010 edition of Wired magazine last week. Today’s links of the day are all from Wired.

(1) “Fill in the Blanks: Using Math to Turn Lo-Res Datasets into High-Res Samples” [Wired] – a fascinating look into the Compressed Sensing algorithm. This article explores how the algorithm, discovered accidentally by Emmanuel Candès, has applications in medical imaging, satellite imaging, and photography. On the origins of the algorithm:

Candès, with the assistance of postdoc Justin Romberg, came up with what he considered to be a sketchy and incomplete theory for what he saw on his computer. He then presented it on a blackboard to a colleague at UCLA named Terry Tao. Candès came away from the conversation thinking that Tao was skeptical — the improvement in image clarity was close to impossible, after all. But the next evening, Tao sent a set of notes to Candès about the blackboard session. It was the basis of their first paper together. And over the next two years, they would write several more.

If you’ve never heard of Terence Tao, you should find out more about him. He’s one of the most brilliant mathematicians alive today (when he was 24, Tao was promoted to full professor at UCLA, the youngest person to achieve full professorship at UCLA; Tao also won the Fields Medal in 2006, equivalent to the Nobel Prize in mathematics). Tao maintains a very popular blog (among mathematics and those who really enjoy math, as the majority of the topics are quite esoteric for the general audience) here.

So how does compressed sensing work?

Compressed sensing works something like this: You’ve got a picture — of a kidney, of the president, doesn’t matter. The picture is made of 1 million pixels. In traditional imaging, that’s a million measurements you have to make. In compressed sensing, you measure only a small fraction — say, 100,000 pixels randomly selected from various parts of the image. From that starting point there is a gigantic, effectively infinite number of ways the remaining 900,000 pixels could be filled in.

So is this a revolutionary technique? The implication, of course, is that you can create something out of nothing. I remain unconvinced whether this technology will be used in digital photography in the future, but I do anticipate that for gathering large data sets, such as in satellite imagery, this technique will become very popular…

(2) “The Future of Money” [Wired] – an excellent, comprehensive piece explaining how the role of paying for things online has evolved since the days of PayPal. This is a must-read if you’re unfamiliar with the history of PayPal, don’t know how credit card transactions are made, and if you haven’t heard of recent developments of TwitPay and/or Square.