The unprecedented growth of the Internet of Things (IoT) has caused wireless sensor networks (WSNs) to receive considerable attention from the research community. WSNs consist of hundreds of limited-resource sensors connected via wireless links. The main purpose of WSN systems is to collect information about their surroundings. First, the sensor nodes gather data from the environment. Subsequently, they transfer these data to a base station (BS) or sink node for processing. Researchers worldwide have been interested in WSNs owing to their low cost and wide variety of applications. WSNs can be used in many terrains, such as land [1], underground [2], and underwater [3]. They also offer great promise for a variety of applications, such as military target tracking and surveillance ^[4][5][4,5], natural disaster relief ^[6][7][6,7], and biomedical health monitoring ^[8][9][8,9].

It is difficult to monitor every sensor node because the majority of them are located in areas that are not easily accessible. Therefore, sensors may malfunction or be exposed to various factors. This leads to noise issues when the WSN operates, which significantly affects the system performance. One study [10] shows that the WSN performance is significantly degraded when receiving and transmitting data via wireless channels that are influenced by noise. The network may experience data loss or corruption.

Many different noise-causing factors exist, and each has a different impact on the system, depending on the environment and the system itself. Therefore, studying the effects of noise is critical for increasing the effectiveness of the entire system. Various sources of noise can interfere with wireless networks. Generally, the noise is caused by internal or external events. Internal events are factors inside the WSN system that produce noise, and they occur when sensor nodes gather and measure information from their surroundings. In contrast, external events are noise-causing factors from the outside. These could include environmental changes, the sudden appearance of an obstruction between the sensor node and the base station, etc. External events mainly impact WSNs when transmitting data from the sensor nodes to the sink nodes.

Although noise reduction in WSNs is not a new research topic, very few studies have specifically investigated noise caused by external events. This motivated us to carefully consider the noise caused by harsh weather conditions, including rain, snow, and fog. These weather conditions were modeled as attenuation models. The impact of these unfavorable weather conditions was considered when data were transferred from the sensor nodes to a sink node. This noise can negatively affect the reliability of the data because it causes some data packets to be lost when transferring from the sensor nodes to the base station. The missing data packets significantly affect the completeness of the data received by the sink node.

Traditional methods to prevent missing data require the sensor to resend the packet data. However, this solution is not desirable because of energy loss, communication delay, and inefficiency. In recent years, missing data reconstruction has become the preferred approach. The process of missing data reconstruction involves the recovery or reconstruction of missing data through the utilization of previously collected data points [11]. Many studies use algorithms for data recovery. However, most of them do not efficiently use the data from readings from the past, present, and neighborhood because the proposed algorithms are relatively simple and ineffective.

In [12], the authors proposed a data reconstruction algorithm that replaces the missing data with the average of the data series, relying on its own data history. This is quite straightforward. An approach based on machine learning was proposed to address this problem by exploring the correlation between data in the sensors [13]. However, traditional machine learning algorithms only calculate the relationship between data from the same sensor and ignore data from neighboring sensors. Therefore, a reconstruction approach based on a convolutional neural network (CNN) emerges as a potential approach for utilizing multiple directions of data from multiple sensors.

A CNN combined with an autoencoder (CAE) is a popular model for reconstructing missing data. This model takes advantage of the spatiotemporal correlations in sensor data; thus, its performance should be better than that of existing data recovery methods. 

In a normal CAE model, before training, the convolution layer and dense layer weights are initialized randomly. However, random weight initialization may cause the optimized loss function to drop into weak local optima when the training is complete. As a result, the performance of the CAE is significantly diminished.

2. Noise-Tolerant Data Reconstruction Based on Convolutional Autoencoder for Wireless Sensor Network

External and internal events play a crucial role in the reliability of data transmissions, and their study has grown increasingly appealing in recent years. Table 1 summarizes recent studies on noise reduction, considering both internal and external events.

2.1. External Events

As mentioned previously, external events mainly affect WSNs when sending packets from sensor nodes to the base station. This section reviews previous studies related to recovering data lost through external events. In [14], the authors employed an approach based on matrix factorization (MF) using any weights to recover the missing time series data. Although this method can be used with numerous attributes, it is extremely complex. A distributed data prediction model was proposed by [12]. The model predicted upcoming measurements and recovered the missing sensor readings that resulted from diffusion faults and sleep schedules. In [15], an approach was proposed to predict missing readings from a sensor node by utilizing matrix completion techniques. The proposed method considers the correlation between sensor nodes to address the randomly missing data. The disadvantage of these algorithms is that they are relatively straightforward and have limited success in discovering the relationship between the data and sensors to recover the missing data. In the study [16], a method for reconstructing missing data was introduced. This method utilized a multiple linear regression (MLR) model that incorporated spatiotemporal correlation. The results demonstrated the effectiveness of the model in terms of the mean absolute error (MAE), mean squared error (MSE), and data reliability. Subsequently, a clustering strategy was employed to compute the internode correlation. Another study [13] proposed a novel approach using deep learning techniques to recover lost measurement data. The recovered signal was highly consistent with the original signal in both the time and frequency domains.

2.2. Internal Events

Jana et al. [21] introduced a framework to identify and address sensor faults, which are missing, spiky, random, and drifting. Initially, a CNN was employed to determine the existence of a fault and classify its specific type. Subsequently, a collection of distinct CAE networks, each specifically trained to correspond to a particular type of fault, was utilized for the purpose of reconstruction. Jeong et al. [18] introduced a data-centric approach involving a bidirectional recurrent neural network (BRNN) to reconstruct sensor data. This approach takes into account the spatiotemporal correlations present among the sensor data. Researchers have investigated data reconstruction techniques based on compressive sensing in order to mitigate the impact of data packet losses in wireless sensor networks [19]. This system uses a compressive sensing technique to rebuild data after a packet loss. The algorithm under consideration demonstrates significant promise within the domain of structural health monitoring. Tay et al. [20] used a recursive graph median filter to simultaneously address impulsive and Gaussian noise. The proposed filter is ideal for sensor networks with low resources because it can be implemented with distributed processing. The data reconstruction scheme proposed by Chen et al. [17] utilizes matrix completion and temporal stability as its foundation. The problem of data reconstruction was initially conceptualized as a matrix completion task, wherein structural noise was taken into account. This approach relied on the identification and utilization of low-rank characteristics inherent in the sensory environmental data. The matrix completion issue was then constrained to achieve short-term stability to further reduce the reconstruction error. To overcome this issue, an algorithm based on the operator splitting technique and the block coordinate descent method was developed.