RT journal article
T1 Analytical Solutions to Minimum-Norm Problems
A1 Campos Jiménez, Almudena
A1 Vílchez Membrilla, José Antonio
A1 Cobos Sánchez, Clemente
A1 García Pacheco, Francisco Javier
A2 Matemáticas
K1 Hilbert space
K1 convex optimization
K1 supporting vector
K1 matrix norm
K1 MRI
AB For G is an element of Rmxn and g is an element of Rm, the minimization min parallel to G psi-g parallel to 2, with psi is an element of Rn, is known as the Tykhonov regularization. We transport the Tykhonov regularization to an infinite-dimensional setting, that is min parallel to T(h)-k parallel to, where T:H -> K is a continuous linear operator between Hilbert spaces H,K and h is an element of H,k is an element of K. In order to avoid an unbounded set of solutions for the Tykhonov regularization, we transform the infinite-dimensional Tykhonov regularization into a multiobjective optimization problem: min parallel to T(h)-k parallel to andmin parallel to h parallel to. We call it bounded Tykhonov regularization. A Pareto-optimal solution of the bounded Tykhonov regularization is found. Finally, the bounded Tykhonov regularization is modified to introduce the precise Tykhonov regularization: min parallel to T(h)-k parallel to with parallel to h parallel to=alpha. The precise Tykhonov regularization is also optimally solved. All of these mathematical solutions are optimal for the design of Magnetic Resonance Imaging (MRI) coils.
PB MDPI
SN 2227-7390
YR 2022
FD 2022-05
LK http://hdl.handle.net/10498/27087
UL http://hdl.handle.net/10498/27087
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026