Speech Bandwidth Extension (BWE) reconstructs missing high frequencies from a band-limited signal. Please note that perceptually important information is often concentrated in short high-frequency (HF) events. Therefore, an effective BWE requires both accurate HF generation and explicit control over where, how often, and in what spectral form HF energy should be produced. To address the above HF supervision, we present HFSWO, a compact complex-spectral Swin-based dual-stream adversarial framework with two newly proposed specialized discriminators: 1. High-Frequency Safeguard Discriminator (HFSD) converts excessive framewise HF-energy ratios into a differentiable safeguard-constraint penalty optimized through a projected primal--dual augmented-Lagrangian update; 2. Weighted Objective Scoring Discriminator (WOSD) learns an interpretable convex objective scoring over spectral flatness, centroid, and rolloff. Our rigorous experiments on VCTK English and MLS French datasets across multiple frequency ranges, including noisy conditions, show significantly improved perceptual scores with 74.6% fewer parameters than the existing baseline AP-BWE, establishing a new baseline in the BWE task in multilingual and multispeaker setups.

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