Saturday, December 03, 2011

The Sensor Calibration Problem (part 2)

In my previous definition of sensor calibration, I forgot to complexify the problem in the case where the signal is known to be sparse in some basis. The previous entry, formulated the calibration problem as if the signal were sparse in the canonical basis. What we are really generally solving for is something like this:

y = (A+E) B x + epsilon

where y is the set of measurements, x is the (unknown or known) probings, A is the measurement matrix as modeled or known, E is the uncertainty associated with elements of A, B is the sparsifying transform and epsilon another error term. Previously, B was the identity.

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