Statistics and Its Interface
Volume 1 (2008)
Detecting the emergence of a signal in a noisy image
Pages: 3 – 12
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.
change-point, sequential detection, image detection
2010 Mathematics Subject Classification
Primary 62L15. Secondary 60G40.