The logarithmic transform is essential in audio signal processing since human auditory perception is approximately logarithmic with respect to magnitude. However, directly incorporating prior knowledge about signals (e.g., harmonic structure) in the log-magnitude domain into optimization problems solved by standard proximal splitting algorithms remains challenging. To address this issue, this paper proposes a novel regularizer termed EPILOG (Exponential Penalty for Imposing priors on LOG-magnitude). EPILOG indirectly imposes prior knowledge on the log-magnitude of a complex-valued signal through regularization of an auxiliary variable that is shown to be linked with the log-magnitude. Furthermore, we derive its variable-wise proximity operators and develop a proximal splitting algorithm using these operators. Experiments on speech dereverberation demonstrate the effectiveness of the proposed regularizer, particularly in promoting cepstral-domain sparsity.

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