Digital watermarking is an emerging technique to protect intellectual property right and to transmit secondary data. Communication of secret messages or verification of watermarking patterns can be achieved by detecting watermarks in received signals. This paper investigates efficient designs of watermarking patterns by minimizing the probability of detection errors. For an encoder with the knowledge of a decoder and with side information from host signals, a small signal approximation is used in designing efficient watermark patterns. For a decoder without the knowledge of the host signal, accurate statistical modeling can help achieving optimal decoding performance. The design method opens the door for seeking efficient watermarks for many watermarking systems.
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