In this paper, a new method of measurement matrix optimization for compressed sensing based on alternating minimization is introduced. The optimal measurement matrix is formulated in terms of minimizing the Frobenius norm of the difference between the Gram matrix of sensing matrix and the target one. The method considers the simultaneous minimization of the mutual coherence indexes including maximum mutual coherence ${\mu }_{max}$, t-averaged mutual coherence ${\mu }_{ave}$ and global mutual coherence ${\mu }_{all}$, and solves the problem that minimizing a single index usually results in the deterioration of the others. Firstly, the threshold of the shrinkage function is raised to be higher than the Welch bound and the relaxed Equiangular Tight Frame obtained by applying the new function to the Gram matrix is taken as the initial target Gram matrix, which reduces ${\mu }_{ave}$ and solves the problem that ${\mu }_{max}$ would be larger caused by the lower threshold in the known shrinkage function. Then a new target Gram matrix is obtained by sequentially applying rank reduction and eigenvalue averaging to the initial one, leading to lower. The analytical solutions of measurement matrix are derived by SVD and an alternating scheme is adopted in the method. Simulation results show that the proposed method simultaneously reduces the above three indexes and outperforms the known algorithms in terms of reconstruction performance.

In this paper, the problem of constructing the measurement matrix in compressed sensing is addressed. In compressed sensing, constructing a measurement matrix of good performance and easy hardware implementation is of interest. It has been recently shown that the measurement matrices constructed by Logistic or Tent chaotic sequences satisfy the restricted isometric property (RIP) with a certain probability and are easy to be implemented in the physical electric circuit. However, a large sample distance that means large resources consumption is required to obtain uncorrelated samples from these sequences in the construction. To solve this problem, we propose a method of constructing the measurement matrix by the Chebyshev chaotic sequence. The method effectively reduces the sample distance and the proposed measurement matrix is proved to satisfy the RIP with high probability on the assumption that the sampled elements are statistically independent. Simulation results show that the proposed measurement matrix has comparable reconstruction performance to that of the existing chaotic matrices for compressed sensing.

High-speed train cable terminals are prone to insulation defects under complex operating conditions. However, traditional detection methods are limited by the scarcity of labeled data and the challenges in extracting features from non-stationary signals. To address this issue, this paper proposes a novel semi-supervised diagnostic paradigm. First, to account for the time-shift characteristics of partial discharge (PD) signals, an adjacency matrix is constructed using dynamic time warping (DTW), converting PD signals into a spatiotemporal graph representation. Second, a fusion architecture combining a Variational Graph Autoencoder (VGAE) and Gated Recurrent Unit (GRU) is designed, where the GRU captures the dynamic evolution characteristics of PD signals. Furthermore, a k-nearest neighbor (KNN) temporal graph reconstruction strategy is proposed to enhance the model’s robustness. In addition, an auxiliary strategy is introduced, integrating the TimeGAN-based temporal augmentation technique, achieving an accuracy of 90.73% with only 10% labeled data. Finally, interpretability analysis using GNNExplainer verifies the effectiveness of the proposed method in detecting cable terminal insulation defects under conditions of limited data availability.

In compressed sensing (CS), a sparse measurement matrix with few nonzero entries is more competitive than a dense matrix in reducing the number of multiplication units. Recent studies indicate that an optimized measurement matrix having low coherence with a specified dictionary can significantly improve the reconstruction performance. This paper considers the optimization problem of the sparse measurement matrix. The optimized sparse measurement matrix is formulated by minimizing the Frobenius norm of the difference between the Gram matrix of the sensing matrix and the target Gram matrix. First, the approach for updating the target Gram matrix is designed to reduce the maximal, average, and global coherence simultaneously. Then, an improved momentum gradient algorithm for updating the sparse measurement matrix is derived to accelerate convergence. On the basis of alternating minimization, two optimization algorithms are proposed. The experimental results show that the proposed algorithms outperform several state‐of‐the‐art methods in terms of reconstruction performance.