Detecting the emergence of a signal in a noisy image

We study sequential change-point detection when observations form a sequence of independent Gaussian random fields, and the change-point is the time at which a signal of known functional form involving a finite number of unknown parameters appears. Building on Siegmund and Yakir (2008), which identifies in a simpler problem a detection procedure of Shiryayev-Roberts type that is asymptotically minimax up to terms that vanish as the false detection rate converges to zero, we compare easily computed approximations to the Shiryayev-Roberts detection procedure with similar approximations to CUSUM type procedures. Although the CUSUM type procedures are suboptimal, our studies indicate that they compare favorably to the asymptotically optimal procedures.