Given the information in the preceding subsections, we are now ready to define the model we use to relate observed SE frames to a truth image. Note that the model is similar to that described earlier by Fraser et al.^{17} The observed frames are expressed in terms of a spatially varying blur operator and a spatially varying geometric warping operator. In particular, observed frame $k$ is given as Display Formula
$fk(x,y)=s\u02dck(x,y){h\u02dck(x,y)[z(x,y)]}+\eta k(x,y),$(19)
where $x$, $y$ are spatial coordinates, $k$ is the temporal frame index, $z(x,y)$ is the ideal image, and $\eta k(x,y)$ is an additive noise term. The geometric warping operator is defined such that Display Formula$\u27e8s\u02dck(x,y)[z(x,y)]\u27e9=g0(x,y)*z(x,y),$(20)
where $\u27e8\xb7\u27e9$ represents a temporal ensemble mean operator. The blurring operator is defined such that Display Formula$\u27e8h\u02dck(x,y)[z(x,y)]\u27e9=hSE(x,y)*z(x,y).$(21)
Using this model, note that the ensemble mean of the observed frames is given by Display Formula$\u27e8fk(x,y)\u27e9=g0(x,y)*hSE(x,y)*z(x,y)=hLE(x,y)*z(x,y).$(22)