Robust CS reconstruction based on appropriate minimization norm

Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly used l1 and l2 norms, provide good results in case of Laplace and Gaussian noise. However, when the signal is corrupted by Cauchy or Cubic Gaussian noise, these norms fail to provide accurate reconstruction. Therefore, in order to achieve accurate reconstruction, the application of l3 minimization norm is analyzed. The efficiency of algorithm will be demonstrated on examples

Localización de fallas en sistemas de transmisión eléctrica usando sensado comprimido

In the present investigation, we develop a methodology that refers to the location of faults in transmission systems using compressed sensing (CS). A model is develop with the advantages of the algorithm Least Squares (LS), Basic Pursuit (BP) and Orthogonal Matching Pursuit (OMP), which provides a sufficiently dispersed vector by convex optimization, making it possible to recover many more dispersed in a stable manner, solving the problem by iterative approaches. To do this, we use the information provided by the phasor measurement units (PMU), intelligent electronic devices that allow us to measure synchrophasors of sine waves of voltage and current deployed in the power electrical system, which, with this method will allow us to find the estimated location of the failure in a timely manner and maximize the observability of the electrical system.. The proposed method is test in the IEEE 9 transmission bus system, is estimated finding the line with problems and the distance at which the failure.En la Presente investigación, se desarrolló una metodología que hace referencia a la localización de fallas en sistemas de transmisión usando Sensado Comprimido (CS), se desarrolló un modelo con las ventajas del algoritmo Least Squares (LS), Basic Pursuit (BP) y Orthogonal Matching Pursuit (OMP), el cual nos proporciona un vector lo suficientemente disperso por optimización convexa, haciendo posible recuperar señales mucho más dispersas de manera estable, resolviendo el problema mediante aproximaciones iterativas. Para ello, se utiliza la información que nos proporciona las unidades de medición fasorial (PMU), dispositivos electrónicos inteligentes que nos permiten medir sincrofasores de ondas sinusoidales de voltaje y corriente desplegadas en el sistema eléctrico de potencia, el cual, con dicho método nos permitirá encontrar la localización estimada de la falla de manera oportuna y maximizar la observabilidad del sistema eléctrico. El método propuesto fue probado en el sistema de 9 barras de la IEEE, encontrando la línea con problemas y la distancia a la que se estima ocurre la falla

Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing with Prior Information

Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in the measurement vector leading to a poor performance when the noise no longer follows the Gaussian assumption but, instead, is better characterized by heavier-than-Gaussian tailed distributions. In this paper, we propose a robust iterative hard Thresholding (IHT) algorithm for reconstructing sparse signals in the presence of impulsive noise. To address this problem, we use a Lorentzian cost function instead of the $L_2$ cost function employed by the traditional IHT algorithm. We also modify the algorithm to incorporate prior signal information in the recovery process. Specifically, we study the case of CS with partially known support. The proposed algorithm is a fast method with computational load comparable to the LS based IHT, whilst having the advantage of robustness against heavy-tailed impulsive noise. Sufficient conditions for stability are studied and a reconstruction error bound is derived. We also derive sufficient conditions for stable sparse signal recovery with partially known support. Theoretical analysis shows that including prior support information relaxes the conditions for successful reconstruction. Simulation results demonstrate that the Lorentzian-based IHT algorithm significantly outperform commonly employed sparse reconstruction techniques in impulsive environments, while providing comparable performance in less demanding, light-tailed environments. Numerical results also demonstrate that the partially known support inclusion improves the performance of the proposed algorithm, thereby requiring fewer samples to yield an approximate reconstruction.Comment: 28 pages, 9 figures, accepted in IEEE Transactions on Signal Processin

Localización de fallas en redes de distribución eléctrica por sensado comprimido (Compressive Sensing)

This article proposes a method for fault localization in distribution networks applying the theory of compressive sensing. The method consists in the deployment of Smart Feeder Meters in the long nodes of a distribution network, which will be in charge of sensing effective voltage magnitudes of the three phases in pre-fault conditions and during the fault The data obtained from the voltage drops form the observation or measurement vector, whose elements are the variations of the voltage magnitudes of the Smart Feeder Meters, the network impedance model forms the base matrix, this information conforms the variables Of input for the application of the standard compressive sensing ℓ1, which seeks to find a sparse or sparse representation vector, that is to say that a vector is obtained which has few elements other than zero, which indicate the estimated location of the node in failure. The main characteristic of the compressive sensing applied to the fault location is that only the voltage magnitudes are needed to obtain excellent results.Este artículo propone un método para localización de fallas en redes de distribución aplicando la teoría del sensado comprimido. El método consiste en el despliegue de Smart Feeder Meters en los nodos a lo largo de una red eléctrica de distribución, que serán los encargados de sensar magnitudes de tensión eficaz de las tres fases en condiciones de pre-falla y durante la falla Los datos obtenidos de las caídas de tensión forman el vector de observación o medida, cuyos elementos son las variaciones de las magnitudes de tensión de los Smart Feeder Meters, el modelo de impedancia de la red forma la matriz base, esta información conforma las variables de entrada para la aplicación del sensado comprimido norma ℓ1, con lo cual se busca encontrar un vector de representación dispersa o escasa, es decir, que se consigue un vector el cual posee pocos elementos distintos de cero, los que indican la localización estimada del nodo en falla. La principal característica del sensado comprimido aplicado a la localización de fallas es que solo se necesita las magnitudes de tensión para obtener excelentes resultados

Robust compressive sensing of sparse signals: A review

Compressive sensing generally relies on the L2-norm for data fidelity, whereas in many applications robust estimators are needed. Among the scenarios in which robust performance is required, applications where the sampling process is performed in the presence of impulsive noise, i.e. measurements are corrupted by outliers, are of particular importance. This article overviews robust nonlinear reconstruction strategies for sparse signals based on replacing the commonly used L2-norm by M-estimators as data fidelity functions. The derived methods outperform existing compressed sensing techniques in impulsive environments, while achieving good performance in light-tailed environments, thus offering a robust framework for CS