New generalized order-K Jacobsthal and Jacobsthal-Lucas numbers and it's application in digital image filtering

In this thesis, the generalized order-k Jacobsthal sequences and initial conditions that were previously defined were taken into consideration, and although this definition constitutes an order-k sequence, it cannot be a generalization of the conventional Jacobsthal sequence for some reasons. Following, generalized order-k number sequences corresponding to second-order Jacobsthal and Jacobsthal-Lucas numbers of the usual form and initial conditions were defined. In addition, some fundamental elementary identities and generator matrices are presented for these new generalizations. The generalized order-k Jacobsthal and Jacobsthal Lucas sequences were used for image filtering in digital image processing. For filtering, Gaussian, Morphological operation with "Motion", Morphological operation with "Disc" specification, Poisson method, and Jacobsthal method were considered. Structural similarity, Multiscale structural similarity, and Peak SNR were used to evaluate the results. Matlab 2021a version was used for the implementation of the proposed method.