Abstarct: Wireless sensor networks represent a highly effective and useful tool for intermittent data gathering and its transmission to the computing center. In the design of wireless sensor networks, the main goal is to minimize the cost of transferring data to the station node (for processing and interpreting data). One of these methods involves transmitting the compressed data to the station. There are several ways to collect data using compression. One way is to use compact measurement theory, which performs two steps of measuring and compressing data simultaneously. In this method, in contrast to the conventional state, instead of directly measuring the signal, the linear composition of the signal samples is implemented. The nodes' energy consumption is mainly baxsed on three phases of measurement, data processing and communication. In previous studies, two stages of transfer and processing have been prioritized over the measurement, but researchers have recently concluded that optimizing the measurement step and reducing the number of samples by timing the measurement model can play a highly effective role in diminishing the costs of such a system. The main goal of this thesis was to improve the timing method of the measurement model baxsed on the compact measurement in order to reduce the number of obtained samples. In the recent methods baxsed on distributed compressed measurements, first a suitable model for obtaining signals from previous data is derived and eventually the signal is collected from a small number of samples and reconstructed in accordance with the learned signal model. The primary problem is to obtain a signal model (dictionary) from incomplete data, which are under compressed measurement at the station node. Therefore, to access the data, it is necessary to interpolate the missing nodes. In this thesis, instead of interpolation baxsed on conventional methods, the dictionary-baxsed learning methods have been adopted. This method is more effective due to the application of dictionaries, as a dictionary contains the statistical characteristics of the data, which enables more accurate interpolation of missing nodes. According to results of the study, the proposed method excels other conventional methods.