Evolutionary hidden information detection by granulation-based fitness approximation

Spread spectrum watermarking (SSW) is one of the most powerful techniques for secure audio or image watermarking. SSW hides information by spreading the spectrum. The hidden information is called the 'watermark' and is added to a host signal, making the latter a watermarked signal. The spreading of the spectrum is carried out by using a pseudorandom noise (PN) sequence. In conventional SSW approaches, the receiver must know both the PN sequence used at the transmitter and the location of the watermark in the watermarked signal for detecting the hidden information. This method has contributed much to secure audio watermarking in that any user, who is not able to access this secrete information, cannot detect the hidden information. Detection of the PN sequence is the key issue of hidden information detection in SSW. Although the PN sequence can be reliably detected by means of heuristic approaches, due to the high computational cost of this task, such approaches tend to be too computationally expensive to be practical. Evolutionary Algorithms (EAs) belong to a class of such approaches. Most of the computational complexity involved in the use of EAs arises from fitness function evaluation that may be either very difficult to define or computationally very expensive to evaluate. This paper proposes an approximate model, called Adaptive Fuzzy Fitness Granulation with Fuzzy Supervisor (AFFG-FS), to replace the expensive fitness function evaluation. First, an intelligent guided technique via an adaptive fuzzy similarity analysis for fitness granulation is used for deciding on the use of exact fitness function and dynamically adapting the predicted model. Next, in order to avoid manually tuning parameters, a fuzzy supervisor as auto-tuning algorithm is employed. Its effectiveness is investigated with three traditional optimization benchmarks of four different choices for the dimensionality of the search space. The effect of the number of granules on the rate of convergence is also studied. The proposed method is then extended to the hidden information detection problem to recover a PN sequence with a chip period equal to 63, 127 and 255 bits. In comparison with the standard application of EAs, experimental analysis confirms that the proposed approach has an ability to considerably reduce the computational complexity of the detection problem without compromising performance. Furthermore, the auto-tuning of the fuzzy supervisor removes the need of exact parameter determination.