Compressive Sensing and L1 Basis Pursuit
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MAC researchers are currently investigating approaches to Compressive Sensing and its
implications for enabling and improving image and signal processing applications. Compressive Sensing is a technique for
acquiring and reconstructing a signal utilizing the prior knowledge that it is sparse or compressible. Often a signal of
interest is embedded in a data set of much higher dimension. Considering the success of lossy compression formats, we witness
that the significant information contained in a data stream may be retained without perceptible loss even when most of the
data is thrown away. This is an example of the concept of signal sparsity which says that a signal’s “information rate” may
often be much smaller than the bandwidth of its carrier. In fact, sparse signals can be represented with many fewer
components on the right basis (or set of coordinates) and as such sub-sampling schemes may be devised to facilitate this.
The design of such schemes is called Basis Pursuit. The collection of information by such sub-sampled methods is called
Compressive Sampling (CS). It has even been shown that low dimensional objects may be recovered precisely from randomly
sub-sampled higher dimensional data streams by understanding the probability density functions generated by the compressive
sampling.
Illustration of Compressive Sensing for Traffic Monitoring
L1 Basis Pursuit can handle extremely challenging problems robustly
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