In this paper, we propose two-dimensional (2-D) frequency
modulated (FM) signals for digital watermarking. The hidden
information is embedded into an image using the binary phase
information of a 2-D FM prototype. The original image is properly
partitioned into several blocks. In each block, a 2-D FM watermark
waveform is used and the watermark information is embedded using
the binary phase. The parameters of the FM watermark are selected
in order to achieve low bit error rate (BER) detection of the
watermark. Detailed study of performance analysis and parameter
optimizations is performed for 2-D chirp signals as an example of
2-D FM waveforms. Experimental results compare the proposed
methods and support their effectiveness.
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