Open AccessPolyharmonic Decomposition of a Digital Image
Author(s) -
Alex Markovsky
Publication year - 2020
Publication title -
trudy meždunarodnoj konferencii po kompʹûternoj grafiki i zreniû "grafikon"
Language(s) - English
Resource type - Journals
ISSN - 2618-8317
DOI - 10.51130/graphicon-2020-1-144-150
Subject(s) - mathematics , linear subspace , decomposition , completeness (order theory) , image (mathematics) , function (biology) , space (punctuation) , polyharmonic spline , algorithm , mathematical analysis , mathematical optimization , computer science , pure mathematics , computer vision , polynomial , ecology , nearest neighbor interpolation , evolutionary biology , linear interpolation , biology , operating system
A decomposition of the space L2(Q) into a direct sum of polyharmonic subspaces is obtained. The completeness of shift systems of the fundamental solution of the polyharmonic equation is proved. A convergent algorithm for solving the problem of separating the polyharmonic component of a function from L2(Q) is developed. The resulting decomposition is applied to some digital image processing problems; the results of computational experiments are presented.