help me retouch the following English with academic styleAssuming that $theta_j$ with an initial value of 0 is used to represent whether the $jth$ frame is reserved to reconstruct the background we

Assuming that $\theta_{j}$ represents whether the $jth$ frame is reserved for reconstructing the background, we initialize its value as 0. If the $jth$ frame is selected, we set $\theta_{j}=1$.