In this paper, we report on the high image quality, large data capacity, and low computational cost of a distributed data embedding watermarking scheme that uses a Max-plus algebra-based Morphological wavelet Transform (MMT). Previously, we evaluated the basic MMT watermarking scheme for image quality and robustness against image compression attacks defined by the Information Hiding and its Criteria (IHC). The proposed distributed data embedding scheme focuses on middle frequency signal-groups after the MMT decomposition process for embedding watermarks. During the experiments for evaluating scheme capability, we processed 12 benchmark images using the proposed watermarking scheme. The proposed method records to increase the Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity index (SSIM) values. For example, the PSNR value of the middle frequency is improved by 6 dB (24 to 30 dB) higher than that of the high-frequency value. The proposed scheme can keep 30 dB for embedding 12 bits of the watermark in the transformed image of all benchmark images. The SSIM value of the middle frequency is about 1.15 (0.88 to 0.98) times higher than the high-frequency value. Thus, all benchmark images of the SSIM values achieve up to 0.5 when the watermark data of 24-bit are embedded using the proposed distributed scheme. The processing performance on the mobile processor is approximately equal to previous studies despite better image quality. The distributed data embedding scheme indicates the possibility of obtaining practical results compared with related studies.

This paper is concerned with the designing a nonlinear filter making use of a pseudo-formal linearization method and Kalman filter approach of constant-gains type for nonlinear systems. We piecewisely linearize the given nonlinear dynamic and measurement equations by a formal linearization method and design linear filters. They are smoothly united into a single nonlinear filter. The efficacy of this filter is shown through numerical examples.