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Bidimensional empirical mode decomposition (BEMD) algorithm, with high adaptive ability, provides a suitable tool for the noisy image processing, and, however, the edge effect involved in its operation gives rise to a problem—how to obtain reliable decomposition results to effectively remove noises from the image. Accordingly, we propose an approach to deal with the edge effect caused by BEMD in the decomposition of an image signal and then to enhance its denoising performance. This approach includes two steps, in which the first one is an extrapolation operation through the regression model constructed by the support vector machine (SVM) method with high generalization ability, based on the information of the original signal, and the second is an expansion by the closed-end mirror expansion technique with respect to the extrema nearest to and beyond the edge of the data resulting from the first operation. Applications to remove the Gaussian white noise, salt and pepper noise, and random noise from the noisy images show that the edge effect of the BEMD can be improved effectively by the proposed approach to meet requirement of the reliable decomposition results. They also illustrate a good denoising effect of the BEMD by improving the edge effect on the basis of the proposed approach. Additionally, the denoised image preserves information details sufficiently and also enlarges the peak signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

Abstract: The treatment of end effects is one of the most important open problems related to the EMD (Empirical Mode Decomposition) method. This work proposes a new approach that couples the mirror expansion with the extrapolation prediction of regression function to solve this problem. The algorithm includes two steps: the extrapolation of the signal through Support Vector (SV) regression at both endpoints to form the primary expansion signal, then the primary signal is further expanded through extrema mirror expansion and EMD is performed on the resulting signal to obtain reduced end effects. If there is not enough length for the signal to meet the need of finding the length of the data available for expanding the signal, a direct extrapolation towards the outside of the signal at the endpoint is executed by the estimate model, and the length of extrapolation points is controlled by the first local extremum. Applications of the proposed approach to the decomposition of a digital modeling signal and three segment signals from the observed earthquake signal by the EMD method are presented, and all of the results are compared with those on the basis of the traditional mirror expansion approach and the extrapolation estimate expansion based on the SV regression, which shows that the most satisfactory result can be obtained for the elimination of end effects in EMD method by mirror image coupled with SV regression. [Copyright &y& Elsevier]