The log-sum function as a penalty has always been drawing widespread attention in the field of sparse problems. However, it brings a non-convex, non-smooth and non-Lipschitz optimization problem that is difficult to tackle. To overcome the problem, an iterative threshold algorithm for the sparse optimization problems with log-sum function is proposed in this paper. For brevity, the sparse optimization problems with log-sum function are named log-sum regularization. Firstly, by introducing an intermediate function to construct another new function, a property theorem about solution for log-sum regularization is established. Secondly, based on the above theorem, the optimal setting rules of the compromising parameters are elaborated, and an iterative log-sum threshold algorithm is proposed. Thirdly, under the situation that the compromising parameters of log-sum regularization are relatively small, it can be proven that the proposed algorithm converges to a local minimizer of log-sum regularization. Finally, a series of simulations are implemented to examine performance of the proposed algorithm, and the results exhibit that the proposed algorithm outperforms the state-of-the-art algorithms.

Mathematically, the autofocusing and imaging model for sparse aperture inverse synthetic aperture radar (ISAR) has an infinite number of solutions, even with the addition of some sparsity constraints. What relationship exists between these infinite solutions should be answered. In addition, some existing approaches suffer from troublesome manual fine-tuning parameters, or high algorithmic complexity, or low reconstruction accuracy. To deal with the above problems, a sparse aperture ISAR autofocusing and imaging method combining phase estimation and log-sum minimization is proposed in this paper, which has high estimation accuracy and computational efficiency, and avoids complicated manual parameter adjustment. Focusing on the model with a phase diagonal matrix and log-sum function, we reveal why there are countless solutions and what relationships exist between them. These features are shared by other models including different regularization functions. Without sparsity prior, the regularization parameter of the algorithm is changed automatically at each iteration accroding to the ratio of the selected element to the maximum absolute value element in an auxiliary matrix, which controls that only a few elements participate in the computation at each iteration. Coupled with the situation that computationally heavy matrix inversion operations are not required, the calculation speed of the approach is greatly boosted. To show the stability of the algorithm, its convergence is proven without any assumptions. Experiments based on both simulation and measurement data demonstrate that compared with the recently proposed algorithms by others, the proposed algorithm can achieve well-focused ISAR images in less than one second and is very efficient to implement.

Inverse synthetic aperture radar (ISAR) imaging of sparse aperture is a challenging problem. Noting the ISAR image generally exhibits strong sparsity, compressive sensing (CS) and sparse signal recovery methods are widely applied for sparse aperture data. However, the existing sparse aperture ISAR imaging algorithms are either computationally heavy or require manual adjustment of too many parameters, which limits their applications in the real-time ISAR imaging system. This paper proposes a high precision and computationally efficient ISAR imaging algorithm for sparse aperture. A generalized CS model with log-sum minimization is first considered for ISAR imaging, and then the iterative log-sum thresholding (ILT) algorithm is utilized to solve the optimization problem, where no large-scale matrix inversion is performed for reducing the computational overhead. Specifically, to efficiently estimate ISAR image sparsity and avoid manually tuning parameters, a modified version of the ILT algorithm is proposed, in which an adjustment strategy of the trade-off parameter λ is adopted. To analyze the influence of different measurement matrix on the imaging algorithm, four sparse sampling patterns, including centralized sampling (CES), block centralized sampling (BCS), equally space sampling (ESS), and random sampling (RAS), are analyzed based on the mutual incoherence property (MIP). Experiments based on both simulated and measured data substantiate that the proposed two algorithms can achieve well-focused ISAR images and are very efficient to implement. In particular, the imaging time of the modified algorithm is less than one second for a matrix dimension of size 256 × 256, which meets the real-time requirements.

To further enhance the recognition accuracy of automatic modulation recognition, improve communication efficiency, strengthen security, and optimize resource management, this paper designs a high-precision hybrid deep learning model featuring early-stage layer fusion. This model combines with Convolutional Neural Networks (CNN), Transformers, and Deep Neural Networks (DNN) to enhance the model’s feature extraction capabilities, thereby improving modulation recognition accuracy. Experiments are performed on RadioML2016.10a and RadioML2018.01a, and the results show that this architecture can effectively combine the advantages of different types of models, making the overall performance more robust and suitable for complex automatic modulation recognition problems.