In this paper, a speech signal noise reduction based on a multiresolution approach referred to as Empirical Mode Decomposition (EMD) [1] is introduced. The proposed speech denoising method is a fully data-driven approach. Noisy signal is decomposed adaptively into oscillatory components called Intrinsic Mode Functions (IMFs), using a temporal decomposition called sifting process. The basic principle of the method is to reconstruct the signal with IMFs previously thresholded using a shrinkage function. The denoising method is applied to speech with different noise levels and the results are compared to wavelet shrinkage. The study is limited to signals corrupted by additive white Gaussian noise.

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Mathematical morphology is a powerful tool for image analysis; however, classical morphological operators suffer from lacks of robustness against noise, and also intrinsic image features are not accounted at all in the process. We propose in this work a new and different way to overcome such limits, by introducing both robustness and locally adaptability in morphological operators, which are now defined in a manner such that intrinsic image features are accounted. Dealing with partial differential equations (PDEs) for generalized Cauchy problems, we show that proposed PDEs are equivalent to impose robustness and adaptability of corresponding sup-inf operators, to structuring functions. Accurate numerical schemes are also provided to solve proposed PDEs, and experiments conducted for both synthetic and real images, show the efficiency and robustness of our approach.

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