## 1 Introduction  
In numerous applications of wireless sensor networks (WSNs), such as wireless body sensor networks (WBSNs) [1], micro-seismic monitoring wireless sensor networks (MMWSNs) [2], and wireless video monitoring systems (WVMSs) [3], sensors face limitations in energy, bandwidth, computational capability, and storage space. To sustain the lifespan of WSNs and conserve their bandwidth, it is crucial to reduce the amount of data transmitted. Compressed sensing (CS) allows for the acquisition of fewer measurements directly at the sensor, significantly reducing the amount of data to be transmitted. Compressed sensing (CS) [4] is a novel signal acquisition and reconstruction technology that has broken through the limit of the Nyquist sampling theory. By utilizing sparsity, CS allows signals to be sampled at rates significantly below the Nyquist rate by projecting them onto a measurement matrix. The original signal can then be efficiently recovered by solving an optimization problem based on the sparse representation of the signal. CS transfers the computational burden from the encoder to the decoder, which is particularly suitable for sensors with constrained computational capabilities. Thanks to these advantages, CS is extensively employed to optimize the measurement process in diverse applications, including synthetic aperture radar (SAR), wireless body area networks [1], the health monitoring of pipelines [5], micro-seismic monitoring [2], and magnetic resonance imaging [6]. One of the core issues of CS is the measurement process. In sensors, the data are projected onto a measurement matrix to reduce the number of required measurements. Considering the limitations in the computational capability and storage space of sensors, the measurement matrix must be simple and efficient. Many measurement matrices have been proposed, primarily falling into two categories: random measurement matrices and deterministic measurement matrices. Initially, random measurement matrices with elements following independent identical distribution (IID) [7] or Bernoulli distribution [8] were proposed. Having been proven to follow the restricted isometry property (RIP) [8] with high probability, they have been extensively researched. Inspired by the fact that symmetric sign ensembles offer computational advantages over Gaussian ensembles, [PERSON] et al. [9] proposed a measurement matrix based on the symmetric sign ensemble and demonstrated that the random sparse measurement matrix follows the RIP with high probability. Although random measurement matrices have good properties, they are often impractical. Furthermore, as they cannot be reproduced, they must be transmitted from the encoder to the decoder and require a large amount of storage space, which is impractical. Deterministic measurement matrices can overcome the limitations of random measurement matrices. Specifically, deterministic sparse measurement matrices consist of only two elements: '0' and '1'. They have low computational complexity and require minimal storage space, making them particularly suitable for resource-restrained sensors. Numerous deterministic sparse measurement matrices have been proposed. [PERSON] [10] proposed a deterministic sparse measurement matrix using finite fields, but its size is constrained to \(p^{2}\times p^{x+1}\) where \(p\) is a prime number and \(r\) is an integer. [PERSON] et al. [11] constructed several types of deterministic measurement matrices based on finite geometry; however, their dimensions are restricted to specific size of \(\left(q^{3}+q^{2}+q+1\right)*\left[\left(q^{2}+1\right)\left(q^{2}+q+1\right) \right]\), \(q^{3}*\left[q^{2}\left(q^{2}+q+1\right)\right]\), \(\left(q^{3}+1\right)*\left[q^{2}\left(q^{2}-q+1\right)\right]\), and \(\left(q^{2}+1\right)*\left[q^{2}\left(q^{2}+1\right)\right]\) where \(q\) is a prime power. [PERSON] et al. [12] and [PERSON] et al. [13] constructed deterministic sparse measurement matrices based on finite geometry and unitary geometry. However, similar to the matrices created by [PERSON] et al.