Second-Order Approximation of the Pseudoinverse for Operator Deconvolutions and Families of Ill-Posed Problems

摘要: We identify a more accurate means of deconvolving compact nondegenerate operators than that provided by independent application standard regularization techniques to individual members the implied continuum first kind integral equations. For problem defined $$ h(x,t) = \int_Y f(x,y)g(y,t)dY, where it is required find g(y,t) given noise-corrupted versions square-integrable f(x,y) and h(x,t), shown greater accuracy results from optimizing solutions for each member sequence equations derived components singular value expansion determined different fixed values t. This result has particular implications treatment bioelectric/biomagnetic source imaging problems, characteristic need perform such deconvolution been previously handled producing an individually regularized solution above equation t in collection ...