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New auditory-inspired speech processing methods are presented in this paper, combining spectral subtraction and two-dimensional non-linear filtering techniques originally conceived for image processing purposes. In particular, mathematical morphology operations, like erosion and dilation, are applied to noisy speech spectrograms using specifically designed structuring elements inspired in the masking properties of the human auditory system. This is effectively complemented with a pre-processing stage including the conventional spectral subtraction procedure and auditory filterbanks. These methods were tested in both speech enhancement and automatic speech recognition tasks. For the first, time-frequency anisotropic structuring elements over grey-scale spectrograms were found to provide a better perceptual quality than isotropic ones, revealing themselves as more appropriate—under a number of perceptual quality estimation measures and several signal-to-noise ratios on the Aurora database—for retaining the structure of speech while removing background noise. For the second, the combination of Spectral Subtraction and auditory-inspired Morphological Filtering was found to improve recognition rates in a noise-contaminated version of the Isolet database.