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arXiv2026

Prox-Friendly Log-Magnitude Prior on Complex-Valued Signal

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.

cs.SD↗

arXiv2023

Versatile Time-Frequency Representations Realized by Convex Penalty on Magnitude Spectrogram

Sparse time-frequency (T-F) representations have been an important research topic for more than several decades. Among them, optimization-based methods (in particular, extensions of basis pursuit) allow us to design the representations through objective functions. Since acoustic signal processing utilizes models of spectrogram, the flexibility of optimization-based T-F representations is helpful for adjusting the representation for each application. However, acoustic applications often require models of \textit{magnitude} of T-F representations obtained by discrete Gabor transform (DGT). Adjusting a T-F representation to such a magnitude model (e.g., smoothness of magnitude of DGT coefficients) results in a non-convex optimization problem that is difficult to solve. In this paper, instead of tackling difficult non-convex problems, we propose a convex optimization-based framework that realizes a T-F representation whose magnitude has characteristics specified by the user. We analyzed the properties of the proposed method and provide numerical examples of sparse T-F representations having, e.g., low-rank or smooth magnitude, which have not been realized before.

eess.SP↗