Problem
Research questions and friction points this paper is trying to address.
log-magnitude domain
proximal splitting algorithms
complex-valued signal
prior knowledge
audio signal processing
Prox-Friendly Log-Magnitude Prior on Complex-Valued Signal
🤖 AI Summary
This study addresses the challenge of incorporating log-magnitude domain priors into standard proximal splitting algorithms. To overcome this limitation, the authors propose EPILOG, an exponential penalty regularizer that innovatively introduces auxiliary variables to establish an analytical connection with the log-magnitude, thereby indirectly enforcing signal priors. Furthermore, a closed-form proximal operator is derived to construct an efficient solver for complex-valued signals. The primary contribution of this work lies in enabling a proximal-friendly treatment of log-domain priors. Experimental results on speech dereverberation validate the effectiveness of the proposed approach, demonstrating significant improvements in cepstral domain sparsity and offering a novel paradigm for complex-valued signal processing.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Log-magnitude prior
Proximal splitting algorithm
Complex-valued signal
Regularizer
Speech dereverberation
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