Accurate forecasting of solar power generation with fine temporal and spatial resolution is vital for the operation of the power grid. However, state-of-the-art approaches that combine machinelearning with numerical weather predictions (NWP) have coarse resolution. In this paper, we take a graph signal processing perspective and model multi-site photovoltaic (PV) production time series as signals on a graph to capture their spatio-temporal dependencies and achieve higher spatial and temporal resolution forecasts. We present two novel graph neural network models for deterministic multi-site PV forecasting dubbed the graph-convolutional long short term memory (GCLSTM) and the graph-convolutional transformer (GCTrafo) models. These methods rely solely on production data and exploit the intuition that PV systems provide a dense network of virtual weather stations. The proposed methods were evaluated in two data sets for an entire year: 1) production data from 304 real PV systems, and 2) simulated production of 1000 PV systems, both distributed over Switzerland. The proposed models outperform state-of-the-art multi-site forecasting methods for prediction horizons of six hours ahead. Furthermore, the proposed models outperform state-of-the-art single-site methods with NWP as inputs on horizons up to four hours ahead.

Recent results in compressed sensing show that a sparse or compressible signal can be reconstructed from a few incoherent measurements. Since noise is always present in practical data acquisition systems, sensing, and reconstruction methods are developed assuming a Gaussian (light-tailed) model for the corrupting noise. However, when the underlying signal and/or the measurements are corrupted by impulsive noise, commonly employed linear sampling operators, coupled with current reconstruction algorithms, fail to recover a close approximation of the signal. In this paper, we propose robust methods for sampling and reconstructing sparse signals in the presence of impulsive noise. To solve the problem of impulsive noise embedded in the underlying signal prior the measurement process, we propose a robust nonlinear measurement operator based on the weighed myriad estimator. In addition, we introduce a geometric optimization problem based on L ₁ minimization employing a Lorentzian norm constraint on the residual error to recover sparse signals from noisy measurements. Analysis of the proposed methods show that in impulsive environments when the noise posses infinite variance we have a finite reconstruction error and furthermore these methods yield successful reconstruction of the desired signal. Simulations demonstrate that the proposed methods significantly outperform commonly employed compressed sensing sampling and reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments.

In the context of next-generation radio telescopes, like the Square Kilometre Array (SKA), the efficient processing of large-scale data sets is extremely important. Convex optimization tasks under the compressive sensing framework have recently emerged and provide both enhanced image reconstruction quality and scalability to increasingly larger data sets. We focus herein mainly on scalability and propose two new convex optimization algorithmic structures able to solve the convex optimization tasks arising in radio-interferometric imaging. They rely on proximal splitting and forward-backward iterations and can be seen, by analogy, with the clean major-minor cycle, as running sophisticated clean-like iterations in parallel in multiple data, prior, and image spaces. Both methods support any convex regularization function, in particular, the well-studied ℓ₁ priors promoting image sparsity in an adequate domain. Tailored for big-data, they employ parallel and distributed computations to achieve scalability, in terms of memory and computational requirements. One of them also exploits randomization, over data blocks at each iteration, offering further flexibility. We present simulation results showing the feasibility of the proposed methods as well as their advantages compared to state-of-the-art algorithmic solvers. Our matlab code is available online on GitHub.

Recent results in telecardiology show that compressed sensing (CS) is a promising tool to lower energy consumption in wireless body area networks for electrocardiogram (ECG) monitoring. However, the performance of current CS-based algorithms, in terms of compression rate and reconstruction quality of the ECG, still falls short of the performance attained by state-of-the-art wavelet-based algorithms. In this paper, we propose to exploit the structure of the wavelet representation of the ECG signal to boost the performance of CS-based methods for compression and reconstruction of ECG signals. More precisely, we incorporate prior information about the wavelet dependencies across scales into the reconstruction algorithms and exploit the high fraction of common support of the wavelet coefficients of consecutive ECG segments. Experimental results utilizing the MIT-BIH Arrhythmia Database show that significant performance gains, in terms of compression rate and reconstruction quality, can be obtained by the proposed algorithms compared to current CS-based methods.

Compressive sensing (CS) is a new approach for the acquisition and recovery of sparse signals that enables sampling rates significantly below the classical Nyquist rate. Based on the fact that electrocardiogram (ECG) signals can be approximated by a linear combination of a few coefficients taken from a Wavelet basis, we propose a compressed sensing-based approach for ECG signal compression. ECG signals generally show redundancy between adjacent heartbeats due to its quasi-periodic structure. We show that this redundancy implies a high fraction of common support between consecutive heartbeats. The contribution of this paper lies in the use of distributed compressed sensing to exploit the common sup port between samples of jointly sparse adjacent beats. Simulation results suggest that compressed sensing should be considered as a plausible methodology for ECG compression.