Suppose we have an 512x512 image, then the value of pixel j should be $I_j = \int_{0}^{512} \int_{0}^{512} h_j(u,v)L(u,v) \,dudv$, where $h_j(u,v)$ is the filter function for pixel j, $L(u,v)$ is the corresponding radiance function.
In practice, we compute the value of pixel j by the formual $\frac{\sum_{i=1}^{N} h_j(u_i,v_i)L(u_i,v_i)}{\sum_{i=1}^{N} h_j(u_i,v_i)}$. Veach said that this estimate is slightly biased in page 308 in his thesis.
So my question is what's the expectation of this estimate?