To investigate the performance of HOSVD in estimating the system error, we simulated the data according to model 2. Poisson random variables $Xi,j,k$ are generated with conditional mean: $B(i,j)+\u2211l=11001000\xb7Fpsil,jl(i,j)gil,jl(k)$, $1\u2264i\u2264256$, $1\u2264j\u2264512$ and $1\u2264k\u226440$. We generated the system error $B(i,j)$, simulating real data; thus, we fitted a bi-variate function $B(i,j)$ on a real image as Display Formula
$B(i,j)=349.8+185.6j^\u2212158.5i^\u22121104.6j^2+929.2i^j^+976.4i^2+2229.5j^3\u22121213.7i^j^2\u2212785i^2j^\u22121490.7i^3\u22121350.3j^4+454.3i^j^3+530.6i^2j^2+117.2i^3j^+675.5i^4,$
with $(i^,j^)=(i/256,j/512)$. We also set $Fpsil,jl$ to be the standard Gaussian distribution centered at the uniformly distributed random indices $(il,jl)$. The minimum distance between $(il,jl)$ is set to be greater than 6. Finally, $gil,jl(k)\u2208{0,1}$ is a step function with dwelling time distributed as an exponential random variable in each state. Precisely, 100 fluorophores intensity were simulated with mean 1000 and the system error with mean 400. The performance of our algorithm is evaluated by maximum error and the mean squared error between $B$ and $BHOSVD$ at $(il,jl)$. We compared our algorithm with the commonly used local subtraction^{5} ($l\xd7l$ LS, $2l+1$ refers to the size of the background) at $(i0,j0)$, which can be specified as Display Formula$BLS(i0,j0,k|l)=(\u2211i,j\u2208Dl(i0,j0)I(i,j,k)\u2212\u2211i,j\u2208Dl\u22121(i0,j0)I(i,j,k))/8l.$
$Dl(i0,j0)$ is defined in Algorithm ^{t3}. The result is shown in Table 1. With 100 replications of simulation, the maximum error obtained by coupling Algorithms ^{t1} and ^{t2} was evaluated to be $13.6\xb11.6$. As contrasted with the signal intensity of 1000, this indicated an error of about 1.3%.