Nov 27, 2013.

We consider some observation operator $H$ defined on the space $X$.

$$ \tilde{\varphi} = T\varphi$$

$$ H\varphi = HT^{-1}T\varphi $$

$$ = H^{\sim}T\varphi = H^{\sim}\varphi^{\sim} $$

such that $H^{\sim}$ is local

By svd $H = U\wedge V^{T}$ where $\wedge$ is a digonal matrix

$$ T = V^{T} and f^{\sim} = U\overline f

$$