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This paper focuses on the watermarking system using a controlled quantization process. We first present a model of the watermark embedding and extracting processes and carry out their analyses. Then we examine the robustness of the watermarking system against common image processing and clarify the reason why detection errors occur in the watermark extracting process. Based on the result, we improve the watermark extracting process and design robust watermarking systems. The improvement is accomplished using a deconvolution filter and neural network techniques. Numerical experiments using the DCT-based watermarking system show good performance as expected by us.