Wired has a report on the excellent work of Allen Yang, John Wright and Yi Ma mentioned earlier (a technique we implemented in one of the Monday Morning Algorithm.) For those readers coming to this site, please note that a similar type of effort has been undertaken by Jort Gemmeke for voice (Using sparse representations for missing data imputation in noise robust speech recognition). For those of you that want to know more from the description given in the Wired article:
The secret sauce in Yang's new method is a mathematical technique for solving linear equations with sparse entries called, appropriately enough, sparse representation
The "solving linear equation with sparse entries" technique is intimately linked to a subject called compressed sensing or compressive sensing this blog is covering. The same technique is used to implement the astounding single pixel camera at Rice. In short, solving this type of system does not involve solving a least-square problem but involves the use of "weirder" techniques that have only recently been unveiled by people like the recent Fields Medalist Terry Tao, Emmanuel Candes, Justin Romberg, David Donoho and many others. A technical view of the rapidly evolving field on the subject can be found here. Reference papers can be found here.
Credit: NASA/JPL/Space Science Institute, A photograph of Thetys, Titan and Saturn released yesterday.
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