On minimax optimal linear transforms for detection with side information in Gaussian setup

We consider the problem of detection with side information to model robust signal hashing for content tracking. The receiver observes corrupted (by additive colored Gaussian noise) message signals and performs detection, knowing the noise statistics and only some partial information about the message set, which is obtained via applying a dimensionality- reducing linear transform (represented by a full-rank matrix) to the messages. We derive the optimal GLRT-rule for the binary detection setup and find the corresponding error probability. Next, under some mild assumptions on the message set, we analytically derive the minimax-optimal linear transform matrix that minimizes the worst (over the set of messages) case error probability.