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?