## 1 Introduction  
The appearance of fifth-generation (5G) technology, which is capable of integrated communication, presents an excellent opportunity to promote resource management that is informed, sustainable, and robust. This technology provides real-time data on the environmental impacts of different behaviors, opening new possibilities for in-depth analytics. The ability to monitor and control systems quickly has facilitated the creation of intelligent environments. In this context, the Internet of Things (IoT) is expected to emerge as a vital component of 5G applications, particularly in the sensing and monitoring domains [1, 2]. The IoT is explicitly designed for massive machine-type communication (mMTC) applications [3], which emphasizes its significance in the changing world of 5G technologies. The IoT is crucial in various fields ranging from environmental monitoring [4, 5, 6] to healthcare systems [7, 8]. These networks offer a cost-effective means of sensing, collecting, and processing environmental information. However, the deployment of IoTs exposes them to potential data corruption resulting from factors such as device failure, signal interference,and adverse environmental conditions [9]. Consequently, reconstructing corrupt data has become crucial for maintaining the precision and reliability of information collected by IoTs in 5G networks. A key consideration in addressing the challenges of data reconstruction is gathering real IoT data. Typically, most recently developed WSN appliances utilize sensors with multiple sensing units to detect different variables such as temperature, pressure, O\({}_{2}\), and NO\({}_{2}\)[10]. Therefore, sensor nodes often collect data with multiple attributes, resulting in multivariate data. In addition, the collected data exhibited spatiotemporal and multivariate correlations. The correlations among these attributes can be leveraged to enhance data reconstruction performance. Despite this promising direction, only one work has delved into multivariate data reconstruction in the IoT [11], with limited success. Using a tensor structure is beneficial for data reconstruction and demonstrates proficiency in harnessing spatiotemporal correlations, particularly for multivariate data. Consequently, traditional methods such as tensor completion (TC) and the tensor robust principal component analysis (TRPCA) [11; 12] have been widely employed for both univariate and multivariate data reconstruction. However, these approaches have limitations. They often ignore differences in singular values, treating them uniformly. In the context of data reconstruction, this oversight may result in suboptimal performance. In practice, the challenges associated with data reconstruction are often complex and involve various forms of corruption, including multiple types of noise, outliers, and missing values. However, previous studies mainly focused on individual types of corruption [11; 13]. The corruption of IoT data can occur owing to various factors, including noise, outliers, and missing values. In this study, we consider two types of noise: Gaussian and impulsive. Gaussian noise is a result of hardware imperfections and computational limitations and follows a Gaussian distribution [14]. By contrast, impulsive noise appears suddenly and disrupts information more intensely [15]. It can be triggered by external factors, such as power surges, electromagnetic interference, and faults in sensor nodes, resulting in abrupt changes and extreme data values. Outliers are values that deviate significantly from the normal range. They indicate severe errors in measurements, such as sensor malfunctions, inaccurate readings, and unexpected events in the environment. Outliers are considered abnormal and can significantly affect the overall behavior of data [16]. Missing values are a common issue in IoT data and can occur for various reasons. Sensor nodes may fail to transmit data owing to hardware failures, network problems, or limited energy resources.