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