Creating Something out of (Next to) Nothing

Normally when creating a digital file, such as a picture, much more
information is recorded than necessary-even before storing or
sending. The image on the right was created with compressed (or
compressive) sensing, a breakthrough technique based on probability
and linear algebra. Rather than recording excess information and
discarding what is not needed, sensors collect the most significant
information at the time of creation, which saves power, time, and
memory. The potential increase in efficiency has led researchers to
investigate employing compressed sensing in applications ranging
from missions in space, where minimizing power consumption is
important, to MRIs, for which faster image creation would allow for
better scans and happier patients. Just as a word has different
representations in different languages, signals (such as images or
audio) can be represented many different ways. Compressed sensing
relies on using the representation for the given class of signals
that requires the fewest bits. Linear programming applied to that
representation finds the most likely candidate fitting the
particular low-information signal. Mathematicians have proved that
in all but the very rarest case that candidate-often constructed
from less than a tiny fraction of the data traditionally
collected-matches the original. The ability to locate and capture
only the most important components without any loss of quality is
so unexpected that even the mathematicians who discovered
compressed sensing found it hard to believe. For More Information:
"Compressed Sensing Makes Every Pixel Count," What's Happening in
the Mathematical Sciences, Vol. 7, Dana Mackenzie.