Wind has been one of the popular renewable energy generation methods in the last decades. Foreknowledge of power to be generated from wind is crucial especially for planning and storing the power. It is evident in various experimental data that wind speed time series has non‐linear characteristics. It has been reported in the literature that nonlinear prediction methods such as artificial neural network (ANN) and adaptive neuro fuzzy inference system (ANFIS) perform better than linear autoregressive (AR) and AR moving average models. Polynomial AR (PAR) models, despite being non‐linear, are simpler to implement when compared with other non‐linear AR models due to their linear‐in‐the‐parameters property. In this study, a PAR model is used for one‐day ahead wind speed prediction by using the past hourly average wind speed measurements of Çeşme and Bandon and performance comparison studies between PAR and ANN‐ANFIS models are performed. In addition, wind power data which was published for Global Energy Forecasting Competition 2012 has been used to make power predictions. Despite having lower number of model parameters, PAR models outperform all other models for both of the locations in speed predictions as well as in power predictions when the prediction horizon is longer than 12 h.

In order to analyze synthetic aperture radar (SAR) images of the sea surface, ship wake detection is essential for extracting information on the wake generating vessels. One possibility is to assume a linear model for wakes, in which case detection approaches are based on transforms such as Radon and Hough. These express the bright (dark) lines as peak (trough) points in the transform domain. In this article, ship wake detection is posed as an inverse problem, which the associated cost function including a sparsity enforcing penalty, i.e., the generalized minimax concave (GMC) function. Despite being a nonconvex regularizer, the GMC penalty enforces the overall cost function to be convex. The proposed solution is based on a Bayesian formulation, whereby the point estimates are recovered using a maximum a posteriori (MAP) estimation. To quantify the performance of the proposed method, various types of SAR images are used, corresponding to TerraSAR-X, COSMO-SkyMed, Sentinel-1, and Advanced Land Observing Satellite 2 (ALOS2). The performance of various priors in solving the proposed inverse problem is first studied by investigating the GMC along with the L₁, Lₚ, nuclear, and total variation (TV) norms. We show that the GMC achieves the best results and we subsequently study the merits of the corresponding method in comparison to two state-of-the-art approaches for ship wake detection. The results show that our proposed technique offers the best performance by achieving 80% success rate.

Synthetic aperture radar (SAR) imagery can provide useful information in a multitude of applications, including climate change, environmental monitoring, meteorology, high dimensional mapping, ship monitoring, or planetary exploration. In this article, we investigate solutions for several inverse problems encountered in SAR imaging. We propose a convex proximal splitting method for the optimization of a cost function that includes a nonconvex Cauchy-based penalty. The convergence of the overall cost function optimization is ensured through careful selection of model parameters within a forward-backward (FB) algorithm. The performance of the proposed penalty function is evaluated by solving three standard SAR imaging inverse problems, including super-resolution, image formation, and despeckling, as well as ship wake detection for maritime applications. The proposed method is compared to several methods employing classical penalty functions such as total variation (TV) and L₁ norms, and to the generalized minimax-concave (GMC) penalty. We show that the proposed Cauchy-based penalty function leads to better image reconstruction results when compared to the reference penalty functions for all SAR imaging inverse problems in this article.

In this paper, we propose a proximal splitting methodology with a non-convex penalty function based on the heavy-tailed Cauchy distribution. We first suggest a closed-form expression for calculating the proximal operator of the Cauchy prior, which then makes it applicable in generic proximal splitting algorithms. We further derive the condition required for guaranteed convergence to the global minimum in optimisation problems involving the Cauchy based penalty function. Setting the system parameters by satisfying the proposed condition ensures convergence even though the overall cost function is non-convex, when minimisation is performed via a proximal splitting algorithm. The proposed method based on Cauchy regularisation is evaluated by solving generic signal processing examples, i.e. 1D signal denoising in the frequency domain, two image reconstruction tasks including de-blurring and denoising, and error recovery in a multiple-antenna communication system. We experimentally verify the proposed convergence conditions for various cases, and show the effectiveness of the proposed Cauchy based non-convex penalty function over state-of-the-art penalty functions such as $L_1$ and total variation ( $TV$ ) norms.