Neural Vocoder Restoration Under Range-Null Space Decomposition

Abstract

The restoration of degraded speech signals has historically relied on either purely generative modeling or deterministic signal processing techniques. While modern neural vocoders achieve exceptional synthesis quality under pristine conditions, they exhibit severe performance degradation when exposed to corrupted, band-limited, or artifact-heavy acoustic inputs. This paper introduces a comprehensive framework for neural vocoder restoration grounded in range-null space decomposition. By formulating the acoustic degradation process as an ill-posed linear inverse problem, we partition the optimization space into two strictly orthogonal components. The range space component guarantees absolute data consistency with the observed degraded signal, preserving the structural integrity and low-frequency semantic content of the original audio. Simultaneously, the null space component acts as a strictly bounded generative pipeline, utilizing deep neural networks to synthesize lost high-frequency details, reconstruct missing harmonics, and eliminate non-linear distortion artifacts without altering the known temporal structure. We extensively evaluate this dual-pathway architecture across a multitude of complex acoustic degradation scenarios, including extreme band-limiting, aggressive clipping, and heavy reverberation. Experimental results indicate that our proposed methodology significantly outperforms traditional end-to-end generative models in both objective metrics and subjective listening tests. Furthermore, we demonstrate that explicit range-null space orthogonalization stabilizes the training of adversarial vocoder architectures, converging faster and mitigating the phenomenon of hallucinated acoustic artifacts commonly observed in unconstrained generative models.