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?