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Microwave imaging techniques allow for the development of systems that are able to inspect, identify, and characterize in a noninvasive fashion under different scenarios, ranging from biomedical to subsurface diagnostics as well as from surveillance and security applications to nondestructive evaluation. Such great opportunities, though, are actually severely limited by difficulties arising from the solution of the underlying inverse scattering problem. As a result, ongoing research efforts in this area are devoted to developing inversion strategies and experimental apparatus so that they are as reliable and accurate as possible with respect to reconstruction capabilities and resolution performance, respectively. The intent of this Special Issue is to present the experiences of leading scientists in the electromagnetic inverse scattering community, as well as to serve as an assessment tool for people who are new to the area of microwave imaging and electromagnetic inverse scattering problems.

joint sparsity --- magnetic resonance imaging --- near-field measurements --- rank minimization --- compressed sensing --- array diagnosis --- microwave plasma diagnostics --- radar-based breast imaging --- image-based approach --- contraction integral equation for inversion (CIE-I) --- nonlinear optimization --- contrast-source inversion --- electromagnetic inverse scattering problems --- nonlinear problem --- tomography --- RCS estimation --- inverse problems --- discontinuous Galerkin method (DGM) --- microwave imaging profilometry --- electrical-property tomography --- breast imaging --- antenna array --- finite-difference methods --- adjoint inversion methods --- Bayesian compressive sensing (BCS) --- orthogonality sampling method --- inverse scattering --- linear sampling method --- breast cancer --- contrast source inversion (CSI) --- imaging --- electromagnetic inverse scattering --- antenna testing --- stopping criteria --- 3D --- microwave imaging --- Kolmogorov-Smirnov (K-S) test --- inverse obstacles problem --- 5G communication --- inverse source problem

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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

structured matrices --- numerical methods --- time fractional differential equations --- hierarchical splines --- finite difference methods --- null-space --- highly oscillatory problems --- stochastic Volterra integral equations --- displacement rank --- constrained Hamiltonian problems --- hyperbolic partial differential equations --- higher-order finite element methods --- continuous geometric average --- spectral (eigenvalue) and singular value distributions --- generalized locally Toeplitz sequences --- Volterra integro–differential equations --- B-spline --- discontinuous Galerkin methods --- adaptive methods --- Cholesky factorization --- energy-conserving methods --- order --- collocation method --- Poisson problems --- time harmonic Maxwell’s equations and magnetostatic problems --- tree --- multistep methods --- stochastic differential equations --- optimal basis --- finite difference method --- elementary differential --- gradient system --- curl–curl operator --- conservative problems --- line integral methods --- stochastic multistep methods --- Hamiltonian Boundary Value Methods --- limited memory --- boundary element method --- convergence --- analytical solution --- preconditioners --- asymptotic stability --- collocation methods --- histogram specification --- local refinement --- Runge–Kutta --- edge-preserving smoothing --- numerical analysis --- THB-splines --- BS methods --- barrier options --- stump --- shock waves and discontinuities --- mean-square stability --- Volterra integral equations --- high order discontinuous Galerkin finite element schemes --- B-splines --- vectorization and parallelization --- initial value problems --- one-step methods --- scientific computing --- fractional derivative --- linear systems --- Hamiltonian problems --- low rank completion --- ordinary differential equations --- mixed-index problems --- edge-histogram --- Hamiltonian PDEs --- matrix ODEs --- HBVMs --- floating strike Asian options --- Hermite–Obreshkov methods --- generalized Schur algorithm --- Galerkin method --- symplecticity --- high performance computing --- isogeometric analysis --- discretization of systems of differential equations