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In this paper, a new technique of Electrocardiogram (ECG) denoising, is introduced and is based on Transformation Matrix for Non-Decimated Wavelet Transform (WT) and Wavelet/Total Variation (WATV) Denoising. It firstly consists of applying twice the Discrete Wavelet Transform (DWT) to the noisy ECG in order to obtain three wavelet coefficients which are the approximation coefficient, cA1 (at level 2) and two details coefficients, cD (at level 1) and cD1 (at level 2). Then, the two coefficients, cD and cD1 are denoised by applying the Transformation Matrix for Non-Decimated WT and we obtain two denoised coefficients, cDd and cDd1. The coefficient, cA1, is also denoised by applying the WATV Denoising and we obtain a third denoised coefficient, cAd1. Finally, the inverse of DWT is twice applied to the three denoised coefficients, cDd, cDd1and cAd1 in order to obtain the denoised ECG signal. The results obtained from the computations of SNR (Signal to Noise Ratio), PSNR (Peak SNR), MSE (Mean Square Error), MAE (Mean Absolute Error) and Cross-Correlation (CC), show the performance of this ECG denoising approach, proposed in this work.

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This paper deals with systems verification techniques, using Bounded Model Checking (BMC). We present a new approach that combines BMC with symmetry reduction techniques. Our goal is to reduce the number of transition sequences, which can be handled by a SAT solver, used in the resolution of verification problems. In this paper, we generate a reduced model by exploiting the symmetry of the original model,which contains only transition sequences that represent the equivalence classes of the symmetric transition sequences. We consider the construction of a new Boolean formula that manipulates only representative transition sequences. In our technique, we present a method that combines the symmetry reduction technique with BMC for the reduction of the space and time of Model Checking.