This study proposes an augmented Lagrange multiplier-based method to perform the singular spectral analysisbased denoising without computing the singular values. In particular, the one-dimensional (1D) signal is first mapped to a trajectory matrix using the window length L. Second, the trajectory matrix is represented as the sum of the signal dominant matrix and the noise-dominant matrix. The determination of these two matrices is formulated as an optimisation problem with the objective function being the sum of the rank of the signal dominant matrix and the l 0 norm of the noise-dominant matrix. This study employs the Schatten q-norm operator with q = 1/2 and the double nuclear-norm penalty for approximating the rank operator as well as the minimum concave penalty (MCP)-norm operator for approximating the l 0-norm operator. Third, some auxiliary variables are introduced and the augmented Lagrange multiplier algorithm is applied to find the optimal solution. Finally, the 1D denoised signal is obtained by applying the diagonal averaging method to the obtained signal dominant matrix. Computer numerical simulation results show that the authors' proposed method outperforms the existing methods.

This paper proposes a framework combining the complementary ensemble empirical mode decomposition with both the independent component analysis and the non-negative matrix factorization for estimating both the heart rate and the respiratory rate from the photoplethysmography (PPG) signal. After performing the complementary ensemble empirical mode decomposition on the PPG signal, a finite number of intrinsic mode functions are obtained. Then, these intrinsic mode functions are divided into two groups to perform the further analysis via both the independent component analysis and the non-negative matrix factorization. The surrogate cardiac signal related to the heart activity and another surrogate respiratory signal related to the respiratory activity are reconstructed to estimate the heart rate and the respiratory rate, respectively. Finally, different records of signals acquired from the Medical Information Mart for Intensive Care database downloaded from the Physionet Automated Teller Machine (ATM) data bank are employed for demonstrating the outperformance of our proposed method. The results show that our proposed method outperforms both the digital filtering approach and the conventional empirical mode decomposition based methods in terms of reconstructing both the surrogate cardiac signal and the respiratory signal from the PPG signal as well as both achieving the higher accuracy and the higher reliability for estimating both the heart rate and the respiratory rate.

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This study proposes a computer cryptographic system through performing the chaotic modulation on the intrinsic mode functions with a non-dyadic number of the encrypted signals. First, the empirical mode decomposition is applied to an input signal to generate a set of intrinsic mode functions. Then, these intrinsic mode functions are categorised into two groups of signals. Next, a type 1 polyphase is employed to represent each group of signals. These polyphase components are combined to generate a non-dyadic number of polyphase components. Second, the chaotic modulation is applied to these combined polyphase components for performing the encryption in the time frequency domain. To reconstruct the original signal, first, the chaotic demodulation is applied to the encrypt components to reconstruct the combined polyphase components. Then, the original groups of intrinsic mode functions are reconstructed through the type 2 polyphase representation and the original signal is reconstructed. Compared with the chaotic filter bank system, the proposed approach enjoys the nonlinear and adaptive property of the empirical mode decomposition. Therefore, a better security performance can be achieved particularly for the non-stationary signals. Compared with the conventional chaotic modulation approach, the proposed system allows performing the cryptography in the time frequency domain.