Federated Learning (FL) enables collaborative training across decentralized data, but faces key challenges of bidirectional communication overhead and client-side data heterogeneity. To address communication costs while embracing data heterogeneity, we propose pFed1BS, a novel personalized federated learning framework that achieves extreme communication compression through one-bit random sketching. In personalized FL, the goal shifts from training a single global model to creating tailored models for each client. In our framework, clients transmit highly compressed one-bit sketches, and the server aggregates and broadcasts a global one-bit consensus. To enable effective personalization, we introduce a sign-based regularizer that guides local models to align with the global consensus while preserving local data characteristics. To mitigate the computational burden of random sketching, we employ the Fast Hadamard Transform for efficient projection. Theoretical analysis guarantees that our algorithm converges to a stationary neighborhood of the global potential function. Numerical simulations demonstrate that pFed1BS substantially reduces communication costs while achieving competitive performance compared to advanced communication-efficient FL algorithms.

Federated learning (FL) is a collaborative machine learning technique to train a global model (GM) without obtaining clients' private data. The main challenges in FL are statistical diversity among clients, limited computing capability among clients' equipment, and the excessive communication overhead between the server and clients. To address these challenges, we propose a novel sparse personalized FL scheme via maximizing correlation (FedMac). By incorporating an approximated $\ell _{1}$ -norm and the correlation between client models and GM into standard FL loss function, the performance on statistical diversity data is improved and the communicational and computational loads required in the network are reduced compared with nonsparse FL. Convergence analysis shows that the sparse constraints in FedMac do not affect the convergence rate of the GM, and theoretical results show that FedMac can achieve good sparse personalization, which is better than the personalized methods based on the $\ell _{2}$ -norm. Experimentally, we demonstrate the benefits of this sparse personalization architecture compared with the state-of-the-art personalization methods (e.g., FedMac, respectively, achieves 98.95%, 99.37%, 90.90%, 89.06%, and 73.52% accuracy on the MNIST, FMNIST, CIFAR-100, Synthetic, and CINIC-10 datasets under non-independent and identically distributed (i.i.d.) variants).

Federated learning faces huge challenges from model overfitting due to the lack of data and statistical diversity among clients. To address these challenges, this paper proposes a novel personalized federated learning method via Bayesian variational inference named pFedBayes. To alleviate the overfitting, weight uncertainty is introduced to neural networks for clients and the server. To achieve personalization, each client updates its local distribution parameters by balancing its construction error over private data and its KL divergence with global distribution from the server. Theoretical analysis gives an upper bound of averaged generalization error and illustrates that the convergence rate of the generalization error is minimax optimal up to a logarithmic factor. Experiments show that the proposed method outperforms other advanced personalized methods on personalized models, e.g., pFedBayes respectively outperforms other SOTA algorithms by 1.25%, 0.42% and 11.71% on MNIST, FMNIST and CIFAR-10 under non-i.i.d. limited data.

A wireless sensing system with n sensors, observing independent and identically distributed continuous random variables with a symmetric probability density function, and one non-collocated estimator acting as a fusion center is considered. The sensors transmit information to the fusion center via a limited capacity communication medium modeled by a collision channel. It is assumed that there is no communication among the sensors prior to transmission, and the collision channel allows at most k < n simultaneous transmissions. Assuming that each sensor uses a symmetric threshold communication strategy, the problem of designing a threshold that minimizes a mean-squared error criterion is considered. Theoretical analysis shows the existence and uniqueness of the optimal threshold for this optimization problem.

Penetrating radar systems are widely employed to scan the objects that are placed behind or buried inside mediums (such as walls, ground, and so on). As the clutter is much stronger than the target echo, clutter removal must be performed before imaging. The moving average subtraction, spatial notch filtering, and singular value decomposition methods are commonly used to remove clutter. However, the drawback is that these methods eliminate some of the target spectrum information, which causes target energy losses and generates side lobes. To solve this problem, two spectrum recovery methods are proposed in this paper. The first method recovers the spectrum magnitude and phase via sinc interpolation and linear fitting, respectively, which is fast and suitable for real-time processing. Although the second method recovers the spectrum based on matrix completion with prior information, which is more accurate and more computational expensive. Extensive simulations and experiments are presented to validate the proposed methods. The results show that the proposed methods can improve various traditional clutter removal methods, the side lobes are clearly suppressed, and the signal-to-clutter ratio is significantly improved.

Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via maximizing the correlation between the prior knowledge and the desired signal. We then present a geometric analysis for the proposed method under sub-Gaussian measurements. Our results reveal that if the prior information is good enough, then the proposed approach can improve the performance of the standard CS. Simulations are provided to verify our results.