Multiple moduli prediction error expansion reversible data hiding

This manuscript considers the distinct prediction error expansion (PEE) of each pixel up to the limit of overflow/underflow in view of embedding a maximum amount of data. A moduli map is created by associating to each pixel its expansion modulus. Since the storing of the expansion moduli map requires more free space than the room provided by the PEE procedure, the quantization of the map is further investigated. The loss by PEE expansion with lower moduli values is expected to be negligible with respect to the gain due to the efficient lossless compression of the simplified map. A linear programming model is introduced in order to select the moduli that maximize the embedding bit-rate. Experimental results for two well-known predictors, the gradient-adjusted predictor (GAP) and the edge-directed predictor (EDP), are provided. The proposed multiple moduli PEE scheme outperforms the high embedding bit-rate reversible data hiding schemes proposed so far. Embedding bit-rates greater than 3 bpp can be obtained.