help me retouch the following English with academic styleIn the updating temporary stage assuming that $theta_j$ with an initial value of 0 is used to represent whether the $jth$ frame is reserved t

In the transitional phase of updating, an assumption is made that $\theta_{j}$, which initially has a value of 0, represents whether the $jth$ frame is chosen to reconstruct the background. $\theta_{j}$ is then assigned a value of 1 when the $jth$ frame is selected.