# A Dual-Branch Speech Enhancement Model with Harmonic Repair
## 1 Introduction  
In both real-world production and living scenarios, as well as modern communication devices, interference with audio signals is inevitable. Part of the interference originates directly from the real-world environments where voice information is collected, and part arises from signal degradation during compression, transmission, and sampling in electronic devices. This phenomenon is referred to as voice degradation. Speech enhancement technologies aim to remove background noise from audio as much as possible while retaining the original speech information. Traditional speech enhancement methods generally work based on statistical signal principles, such as spectral subtraction [1], minimum mean square error estimation [2], filtering methods including Wiener filter [3] and Kalman filter [4], and subspace enhancement methods that use cross-spectral pairs for frequency filtering of subspace signals [5]. However, these traditional methods often struggle to effectively reduce noise, especially in the presence of multiple noise sources or when the noise frequency range is concentrated. To devise a more versatile filtering method, [PERSON] proposes an approach based on fractional calculus [6], aiming to address setting \(\alpha\)-stable statistics more effectively, which provides an alternative solution to the requirements of modern filtering applications. Currently, the mainstream speech enhancement methods based on deep learning follow two technical approaches. One is time-domain-based, utilizing neural networks to directly infer the spectrum of pure speech from noisy speech, which may produce better harmonic results but require more computational resources and may be less effective in suppressing non-stationary noise compared to time-frequency domain methods [7]. Time-domain methods for waveform processing can significantly improve the Signal-to-Distortion Ratio (SDR) [8], but they may lead to a decrease in auditory perception. Theprimary reason for this issue is that the system, working in only one transform domain, struggles to filter out redundant information in the background noise. The other approach is frequency-domain-based, typically using masking techniques. The basic idea is to combine speech and noise signals in a certain way so that the predicted mask can accurately separate speech and noise signals. Complex Ideal Ratio Mask (CIRM), based on Fourier transformation and the concept of a crude ideal ratio mask, not only considers amplitude information but also phase information to preserve the phase information of the original speech signal and avoid signal distortion due to amplitude changes [9]. Previous research often underestimates the importance of phase information in speech repair, leading to unavoidable speech distortion in denoised speech, which significantly interferes with subsequent speech recognition and speaker recognition tasks, reducing their performances. [PERSON] et al. demonstrate [10] that better utilization of phase information in speech signals can significantly improve the quality of enhanced speech, achieving better performances with less loss. Direct estimation of phase information in spectrograms is challenging, often resulting in large neural networks [11]. To allow the phase information of the speech to play a greater role in the denoising process, researchers have made a considerable amount of effort. Inspired by the [PERSON] series, [PERSON] [12] and others propose a decoupled speech enhancement framework, dividing the optimization problem of the complex spectrum into two parts: the optimization problem of the magnitude spectrum and the estimation of complex residues. To refine the phase distribution, they define the difference between the rough spectrum and the target spectrum to measure the phase gap. A dual-branch enhancement network is introduced in [13], where the complex spectrum refinement branch collaboratively estimates the amplitude and phase information of speech by taking in both the real and imaginary parts.