Learning nonlocal regularization operators

<p style='text-indent:20px;'>A learning approach for determining which operator from a class of nonlocal operators is optimal the regularization an inverse problem investigated. The considered motivated by use squared fractional order Sobolev seminorms as operators. First fundamental results theory with local are extended to case. Then framework based on bilevel optimization strategy developed allows choose given i) respect suitable performance measure training set, and ii) enjoy particularly favorable properties. Results numerical experiments also provided.</p>