## 1 Introduction  
PD signal is a crucial component of monitoring electrical equipment and can accurately reflect the severity of insulation deterioration [1]. Engineers can evaluate the safety and stability of high-voltage equipment using the PD signal. However, due to the complexity of the engineering work environment, PD signals will inevitably be contaminated with various types of noise. White Gaussian noise and narrowband noise have the most significant impact on PD signals [2]. How to eliminate noise, determine the edge, and precisely extract the waveform of PD signals are currently essential research issues.  
In PD signal extraction, PD signals are often polluted by various forms of noise interferences, including continuous periodic noise like system harmonics, impulse interferences from power electronics, and random disturbances such as corona discharges. Additionally, white noise, encompassing thermal and ground network disturbances, further complicates signal clarity. Effective noise mitigation is essential for precise PD signal analysis [3].  
Currently, some traditional signal denoising techniques are employed for noise reduction in PD signals, including Wavelet Transform (WT) [4], Empirical Modal Decomposition (EMD) [5], and SVD [6]. WT is recognized for its proficient time-frequency analysis capabilities, but selecting an optimal wavelet basis for signal decomposition remains challenging, and the choice of wavelet basis and decomposition level significantly affects the denoising outcome [7]. In contrast to WT, EMD generates basic functions directly from the signal,offering adaptive decomposition into multiple modal components with notable robustness. However, EMD can encounter modal aliasing issues, which can hinder effective noise reduction [8]. SVD is also always applied for noise suppression, but it requires manual determination of effective singular value orders, making the process susceptible to human error [9]. In recent research on denoising PD signals, researchers have increasingly turned to advanced and hybrid versions of traditional algorithms such as the AEEMD algorithm [10], the integration of SVD with the VMD algorithm [11], and the Adaptive Wavelet Multilevel Soft Threshold algorithm [12].  
VMD improves upon the traditional EMD method, offering enhanced noise filtering, especially for white noise in vibration signals. The choice of VMD parameters critically affects the quality of the decomposition outcome [13], and a mix of other methods is needed to suppress periodic interference and white noise effectively [14]. Sparse Dictionary Learning, a machine learning algorithm that combines the principles of sparse representation and dictionary learning, has recently gained traction in signal processing. This sparse dictionary learning algorithm is divided into two distinct types: the Analysis Dictionary algorithm and Learning Dictionary algorithm. Although the structure of analysis dictionary is easy to access, the construction of prior knowledge depends on the target signal, which has limitations on the unknown fault features [15]. Denoising algorithms based on analysis dictionaries have been applied in PD signal denoising [16; 17]. However, the learning dictionary method exemplified by the K-SVD algorithm has been unexplored in signal processing.