Recovering high-frequency components lost to bandwidth constraints is crucial for applications ranging from telecommunications to high-fidelity audio on limited resources. We introduce NDSI-BWE, a new adversarial Band Width Extension (BWE) framework that leverage four new discriminators inspired by nonlinear dynamical system to capture diverse temporal behaviors: a Multi-Resolution Lyapunov Discriminator (MRLD) for determining sensitivity to initial conditions by capturing deterministic chaos, a Multi-Scale Recurrence Discriminator (MS-RD) for self-similar recurrence dynamics, a Multi-Scale Detrended Fractal Analysis Discriminator (MSDFA) for long range slow variant scale invariant relationship, a Multi-Resolution Poincaré Plot Discriminator (MR-PPD) for capturing hidden latent space relationship, a Multi-Period Discriminator (MPD) for cyclical patterns, a Multi-Resolution Amplitude Discriminator (MRAD) and Multi-Resolution Phase Discriminator (MRPD) for capturing intricate amplitude-phase transition statistics. By using depth-wise convolution at the core of the convolutional block with in each discriminators, NDSI-BWE attains an eight-times parameter reduction. These seven discriminators guide a complex-valued ConformerNeXt based genetor with a dual stream Lattice-Net based architecture for simultaneous refinement of magnitude and phase. The genertor leverage the transformer based conformer's global dependency modeling and ConvNeXt block's local temporal modeling capability. Across six objective evaluation metrics and subjective based texts comprises of five human judges, NDSI-BWE establishes a new SoTA in BWE.

翻译：恢复因带宽限制而丢失的高频分量，对于从电信到资源受限环境下的高保真音频等应用至关重要。本文提出了NDSI-BWE，一种全新的对抗式带宽扩展（BWE）框架。该框架借鉴非线性动力系统，设计了四个新型判别器以捕捉不同的时间行为：多分辨率Lyapunov判别器（MRLD），通过捕捉确定性混沌来判定对初始条件的敏感性；多尺度递归图判别器（MS-RD），用于捕捉自相似的递归动力学；多尺度去趋势波动分析判别器（MSDFA），用于捕捉长程缓变尺度不变关系；多分辨率庞加莱图判别器（MR-PPD），用于捕捉隐藏的潜在空间关系；多周期判别器（MPD），用于捕捉周期模式；多分辨率幅度判别器（MRAD）和多分辨率相位判别器（MRPD），用于捕捉复杂的幅度-相位转换统计特性。通过在每个判别器的卷积块核心采用深度可分离卷积，NDSI-BWE实现了八倍的参数缩减。这七个判别器共同引导一个基于复数ConformerNeXt的生成器，该生成器采用双流Lattice-Net架构，同时优化幅度和相位。该生成器利用了基于Transformer的Conformer的全局依赖建模能力以及ConvNeXt块的局部时间建模能力。在六项客观评估指标及包含五位人类评审员的主观测试中，NDSI-BWE在BWE领域确立了新的最先进（SoTA）水平。