Band-wise audio denoising via L1pTV optimization for transient noise suppression

We explore audio denoising based on L1-norm fidelity and p-norm total variation (TV) regularization, motivated by the need to suppress sharp transient noise while preserving perceptual features such as speech clarity. Our current approach applies the hyperplane traversal algorithm of Moon and Asaki in the p = 1 regime, with planned extensions to incorporate cluster-prioritized updates for regions with concentrated transient energy. Prior to denoising, the signal is decomposed across frequency bands, enabling localized control of regularization strength and improved adaptation to signal structure. We report on preliminary experiments and discuss tradeoffs encountered in balancing fidelity and smoothness in this band-wise setting.