Suppose we want to recover an input vector
from corrupted measurements
. Note that
is an
matrix and
is a matrix of unknown errors. So then we can recover
exactly from the data
by first identifying the error and subtracting it off. Then we need something that annihilates
so that we can get
. In other words, we want a function such that:
.
In other words, we are looking at the kernel of
. So once we identity the error term...can we recover
exactly? Because given
and
, we want to get
. So ultimately we want to do the following:
- Identify and subtract error term:
- Now we are left with . So we want something that annihilates .
Is this possible?