In this work, a biologically-inspired denoising method for audio signals is presented, which takes advantage of an approximation to the acoustical signal representation at the auditory cortical level. It is based on an optimal dictionary of atoms, estimated from early auditory spectrograms, and the Basis Pursuit algorithm to approximate the cortical activations. The proposed approach employs non-negative sparse coding to pursue a simplified denoising algorithm which exploits a priori information from both clean signals and noise. The method was applied to artificial signals constructed from simultaneous chirps, corrupted with additive noise. Results showed that using an objective quality measure, the method proposed here can improve the audio quality when it is applied to noisy signals.