Implementation of the LARS method to solve the inverse problem in electrical tomography

The presented research presents a method of using the smallest angles regression algorithm to solve the inverse problem in electrical impedance tomography in relation to a damp wall. Highly correlated predictors in linear models make it difficult to precisely determine the influence of these predictors on the output variable. The standard application of the least-squares method to estimate unknown parameters may lead to a poor forecast. Adding a penalty parameter depending on quantities of parameters to the least square criterion allows us to determine the biased estimators but also to reduce the variance of estimators. Streszczenie. Przedstawione badania dotyczą sposobu wykorzystania algorytmu regresji najmniejszego kąta (LARS) do rozwiązania problemu odwrotnego w elektrycznej tomografii impedancyjnej w odniesieniu do wilgotnej ściany. Wysoce skorelowane predyktory w modelach liniowych utrudniają precyzyjne określenie wpływu tych predyktorów na zmienną wyjściową. Standardowe zastosowanie metody najmniejszych kwadratów do oszacowania nieznanych parametrów może prowadzić do złej prognozy. Dodanie elementu kary w zależności od ilości parametrów do kryterium najmniejszego kwadratu pozwala nam określić estymatory obciążenia, a także zmniejszyć wariancję estymatorów. (Implementacja metody LARS do rozwiązywania problemu odwrotnego w tomografii elektrycznej).

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