Rate-Optimal Detection of Very Short Signal Segments
This work addresses detection challenges in engineering and genomics, providing theoretical foundations and practical detectors for short signal segments.
The paper tackles the problem of detecting very short signal segments in three settings: known shape, arbitrary, and smooth signals, establishing optimal detection rates and constructing rate-optimal detectors based on scanning with linear and quadratic statistics.
Motivated by a range of applications in engineering and genomics, we consider in this paper detection of very short signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals. Optimal rates of detection are established for the three cases and rate-optimal detectors are constructed. The detectors are easily implementable and are based on scanning with linear and quadratic statistics. Our analysis reveals both similarities and differences in the strategy and fundamental difficulty of detection among these three settings.