Variance

In the above example, the assumption that the variance of our noise is spatially invariant is correct. In a more general problem, this will not be the case. As a result, a more appropriate formulation for our noise covariance is

$$\bf N= \bf N_c \bf N_v .$$ (11)

In this formulation, $\bf N_c$ is a description of the relation between points. It will take the form of a PEF or one of the other operators described above. The second operator $\bf N_v$ will attempt to normalize the variance of the various data errors to the same level and should be equal to

$$N(i)=\sqrt { \frac{1}{V(i)}} ,$$ (12)

where V(i) is the variance at a given data location i.