## 1 Introduction  
Online monitoring of mechanical equipment status is essential to extend equipment service life and ensure operational safety. However, general industrial equipment operated for a long time, and parts deteriorated slowly. With the increase in monitoring points and monitoring time, there are issues such as storage and transmission difficulties after the gradual accumulation of monitoring data [1, 2]. Faced with this challenge, the industry urgently needs a reliable data compression method to effectively manage and store these large-scale monitoring data. In 2006, [PERSON] proposed compressed sensing (CS) [3], which provides a new idea for large-scale data storage and transmission. CS theory believes that if the signal itself is sparse or has a sparse property under a set of bases or dictionaries, then CS can recover the signal at a sampling rate significantly lower than the sampling rate specified by Nyquist theory [4, 5, 6, 7]. In recent years, CS technology has developed rapidly and is widely used in quite a few fields, such as image processing [8, 9], wireless communication [10], direction of arrival (DOA) estimation [11], and pipeline leakage detection [12]. Especially in industrial production, the CS reconstruction method based on acoustic emission signals [13, 14, 15] and multi-source composite fault signals [16, 17] solved many practical industrial problems. These methods are generally applicable to the operation of mechanical equipment indoors or in stable environmental conditions, and signal acquisition is relatively easy to meet the sparse conditions of the compressed measurement. However, for mechanical equipment required to work in an open environment, the acquisition of monitoring signals is very vulnerable to environmental noise or human factors, such as fluctuation conditions [18; 19], missing data from acquired signals [20; 21; 22], and high-noise interference [23], which results in the acquired signals not accurately reflecting the corresponding fault feature information. In response to high-noise outdoor working conditions, some mechanical equipment monitoring and reconstruction methods have emerged. Generally, these methods are related to optimization-based methods [24; 25], such as sparse optimization methods [26; 27; 28; 29; 30; 31], waveform matching and dictionary learning-based methods [32; 33; 34; 35], and multi-sensor fusion-based methods [36]. Although the need for accurate reconstruction of industrial vibration signals can be effectively addressed by the signal reconstruction methods described above, the disadvantages of the traditional method, such as having many parameters, slow convergence speed, and being prone to significant error at high compression ratios [37; 38; 39], are still difficult to avoid, resulting in the theory not being applied to the online monitoring demand of actual production equipment. Recently, with the continuous development of deep learning, some scholars have proposed the application of neural networks to CS signal reconstruction, aiming to make full use of the advantages of neural networks to compensate for the shortcomings of traditional reconstruction algorithms. This work is usually divided into two main categories: data-driven methods and model-driven methods. The data-driven approach adapts to the data structure by adjusting the network models, such as DR2-Net networks [40], Deep Inverse networks [41], and CSNet networks [42]. The model-driven method is an idea that unfolds traditional CS methods into learning networks, first proposed in 2010 [43]. The article establishes the Learned Iterative Shrinkage Threshold Algorithm (LISTA) model on the basis of the ISTA [44] to solve sparse encoding problems. Since then, this idea has been widely applied to many signal and image problems [45; 46; 47]. In addition to the LISTA model, researchers also proposed unfolded network models such as ISTA-NET [48], LADM-NET [49], and AMP-Net [50].