The/. headline and the Wired article do tend to misrepresent Compressed Sensing as some kind of noise-remover, despeckler, or image enhancer. This is simply not the case. In Compressed Sensing, we are intentionally sampling a signal in an incoherent domain so that each measurement evaluates the entire image globally. In other words, each sample has as much weight as any other, so when we hold on to fewer of them, we may obtain more information about the original signal than if we sub-sampled the signal in the original domain. When we reconstruct the original image from our compressed/sub-sampled measurements in an incoherent domain, we are trying to find the most sparse signal that matches the measurements we observed (solving an ill-posed inverse problem via constrained optimization). The signal sparsity can be thought of the orderedness or "structured-ness" of the signal. In other words, the most ordered image that matches our compressed measurements is correct solution with high degree of probability. For a technical primer, check out this paper ( http://dsp.rice.edu/sites/dsp.rice.edu/files/cs/CSintro.pdf ).
Okay, yes, that might be a little bit weighty if you aren't in the field, but I would suggest you check out Nuit Blanche ( http://nuit-blanche.blogspot.com/ ) for a description of what exactly CS is, how it works, and what it is useful for. Today's article is especially interesting in this regard.
Slashdot Mirror
The /. headline and the Wired article do tend to misrepresent Compressed Sensing as some kind of noise-remover, despeckler, or image enhancer. This is simply not the case. In Compressed Sensing, we are intentionally sampling a signal in an incoherent domain so that each measurement evaluates the entire image globally. In other words, each sample has as much weight as any other, so when we hold on to fewer of them, we may obtain more information about the original signal than if we sub-sampled the signal in the original domain. When we reconstruct the original image from our compressed/sub-sampled measurements in an incoherent domain, we are trying to find the most sparse signal that matches the measurements we observed (solving an ill-posed inverse problem via constrained optimization). The signal sparsity can be thought of the orderedness or "structured-ness" of the signal. In other words, the most ordered image that matches our compressed measurements is correct solution with high degree of probability. For a technical primer, check out this paper ( http://dsp.rice.edu/sites/dsp.rice.edu/files/cs/CSintro.pdf ).
Okay, yes, that might be a little bit weighty if you aren't in the field, but I would suggest you check out Nuit Blanche ( http://nuit-blanche.blogspot.com/ ) for a description of what exactly CS is, how it works, and what it is useful for. Today's article is especially interesting in this regard.