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In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, Lq regularization with q\in(0,1)) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency. As compared with the convex regularization approaches (say, L1 regularization), however, the convergence issue of the corresponding algorithms are more difficult to tackle. In this paper, we deal with this difficult issue for a specific but typical nonconvex regularization scheme, the L1/2 regularization, which has been successfully used to many applications. More specifically, we study the convergence of the iterative half thresholding algorithm (the half algorithm for short), one of the most efficient and important algorithms for solution to the L1/2 regularization. As the main result, we show that under certain conditions, the half algorithm converges to a local minimizer of the L1/2 regularization, with an eventually linear convergence rate. The established result provides a theoretical guarantee for a wide range of applications of the half algorithm. We provide also a set of simulations to support the correctness of theoretical assertions and compare the time efficiency of the half algorithm with other known typical algorithms for L1/2 regularization like the iteratively reweighted least squares (IRLS) algorithm and the iteratively reweighted l1 minimization (IRL1) algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, a novel method for synthetic aperture radar (SAR) imaging is proposed. The approach is based on L regularization to reconstruct the scattering field, which optimizes a quadratic error term of the SAR observation process subject to the interested scene sparsity. Compared to the conventional SAR imaging technique, the new method implements SAR imaging effectively at much lower sampling rate than the Nyquist rate, and produces high-quality images with reduced sidelobes and increased resolution. Also, over the prevalent greedy pursuit and L regularization based SAR imaging methods, there are remarkable performance improvements of the new method. On one hand, the new method significantly reduces the number of measurements needed for reconstruction, as supported by a phase transition diagram study. On the other hand, the new method is more robust to the observation noise. These fundamental properties of the new method are supported and demonstrated both by simulations and real SAR data experiments. [ABSTRACT FROM AUTHOR]

Rank aggregation with pairwise comparisons is widely encountered in sociology, politics, economics, psychology, sports, etc. Given the enormous social impact and the consequent incentives, the potential adversary has a strong motivation to manipulate the ranking list. However, the ideal attack opportunity and the excessive adversarial capability cause the existing methods to be impractical. To fully explore the potential risks, we leverage an online attack on the vulnerable data collection process. Since it is independent of rank aggregation and lacks effective protection mechanisms, we disrupt the data collection process by fabricating pairwise comparisons without knowledge of the future data or the true distribution. From the game-theoretic perspective, the confrontation scenario between the online manipulator and the ranker who takes control of the original data source is formulated as a distributionally robust game that deals with the uncertainty of knowledge. Then we demonstrate that the equilibrium in the above game is potentially favorable to the adversary by analyzing the vulnerability of the sampling algorithms such as Bernoulli and reservoir methods. According to the above theoretical analysis, different sequential manipulation policies are proposed under a Bayesian decision framework and a large class of parametric pairwise comparison models. For attackers with complete knowledge, we establish the asymptotic optimality of the proposed policies. To increase the success rate of the sequential manipulation with incomplete knowledge, a distributionally robust estimator, which replaces the maximum likelihood estimation in a saddle point problem, provides a conservative data generation solution. Finally, the corroborating empirical evidence shows that the proposed method manipulates the results of rank aggregation methods in a sequential manner.

Background: Low physical activity is a major risk factor for cardiovascular diseases (CVDs). This study aimed to estimate the global, regional, national, and sex-age-specific burden of CVDs attributed to low physical activity from 1990 to 2019., Methods: We leveraged data from the Global Burden of Disease Study 2019 to compute the number of fatalities, disability-adjusted life years (DALYs), age-adjusted mortality rates (ASMR), and age-adjusted DALY rates (ASDR) attributed to CVDs resulting from low physical activity. Furthermore, we scrutinized the trends and correlations of these metrics in connection with the socio-demographic index (SDI) across 21 regions and 204 countries and territories., Results: The global deaths and DALYs due to CVDs caused by low physical activity increased from 371,042.96 [95 % UI: 147,621.82-740,490] and 6,282,524.95 [95 % UI: 2,334,970.61-13,255,090.08] in 1990 to 639,174.92 [95 % UI: 272,011.34-1,216,528.4] and 9,996,080.17 [95 % UI: 4,130,111.16-20,323,339.89] in 2019, respectively. The corresponding ASMR and ASDR decreased from 12.55 [95 % UI: 5.12-24.23] and 181.64 [95 % UI: 71.59-374.01] in 1990 to 8.6 [95 % UI: 3.68-16.28] and 127.52 [95 % UI: 53.07-256.55] in 2019, respectively. Deaths and DALYs attributed to low physical activity were initially higher in males but shifted to females after 70-74 age group. Both genders had increasing death rates, peaking at 80-84 age group. Most CVDs deaths and DALYs number are caused by ischemic heart disease. The highest burden of CVDs attributed to low physical activity was observed in North Africa and the Middle East. The lowest burden was observed in Oceania and High-income Asia Pacific. There was a distinctive 'n-shape' relationship between the regional SDI and the ASDR of CVDs attributed to low physical activity from 1990 to 2019., Conclusion: The global impact of CVDs stemming from low physical activity remains substantial and demonstrates substantial regional disparities. As individuals age, this burden becomes more prominent, particularly among females. Efficacious interventions are imperative to promote physical activity and mitigate the risk of CVDs across diverse populations and regions., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

Coded aperture snapshot spectral imaging (CASSI) is an important technique for capturing three-dimensional (3D) hyperspectral images (HSIs), and involves an inverse problem of reconstructing the 3D HSI from its corresponding coded 2D measurements. Existing model-based and learning-based methods either could not explore the implicit feature of different HSIs or require a large amount of paired data for training, resulting in low reconstruction accuracy or poor generalization performance as well as interpretability. To remedy these deficiencies, this paper proposes a novel HSI reconstruction method, which exploits the global spectral correlation from the HSI itself through a formulation of model-driven low-rank subspace representation and learns the deep prior by a data-driven self-supervised deep learning scheme. Specifically, we firstly develop a model-driven low-rank subspace representation to decompose the HSI as the product of an orthogonal basis and a spatial representation coefficient, then propose a data-driven deep guided spatial-attention network (called DGSAN) to adaptively reconstruct the implicit spatial feature of HSI by learning the deep coefficient prior (DCP), and finally embed these implicit priors into an iterative optimization framework through a self-supervised training way without requiring any training data. Thus, the proposed method shall enhance the reconstruction accuracy, generalization ability, and interpretability. Extensive experiments on several datasets and imaging systems validate the superiority of our method. The source code and data of this article will be made publicly available at https://github.com/ChenYong1993/LRSDN.