Assessment of regularization techniques used in solving the ill-posed inverse problem of electrocardiography
Milanič, Matija ; Jazbinšek, Vojko ; Hren, Rok
V tem delu smo sistematično ocenili različne regularizacijske tehnike, ki se uprabljajo pri reševanju slabo pogojenega inverznega problema v elektrokardigrafiji. Za simulacijo potencilanih ...porazdelitev smo uporabili analitično rešljiv model tokovnega dipola znotraj homogenega izotropnega prevodnika sestavljenega iz dveh koncentričnih krogel. Analitično izračunane potenciale na površini večje od obeh krogel (potenciali na "telesu") smo uporabili kot vhodne podatke za določitev potencialov na manjši krogli (potenciali na "srcu"). V celoti smo preiskali 10 različnih regularizacijskih tehnik in rezultate statistično ocenili z normalizirano povprečno kvadratno napako in korelacijskim koeficientom. Ugotovili smo, da tri regularizaijske metode prvega reda - Tihonova (FOT), konjugirani gradient (FCG) in najmanjši kvadrat (FLSQR) - najbolj natančno rekonstruirajo potenciale na "src" z relativnimi napakami med 0.07 in 0.16 ter korelacijskimi koeficienti med 0,991 in 0,999 za rezlične dipolne izvore.
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