Error bounds for extended source inversion applied to an acoustic transmission inverse problem

A simple inverse problem for the wave equation requires determination of both velocity in a homogenous acoustic material and transient waveform an isotropic point radiator, given time history wavefield at remote space. The duration (support) source source-to-receiver distance are assumed known. least squares formulation this exhibits "cycle-skipping" behaviour observed field scale problems type, with many local minima differing greatly from global minimizer. An extended formulation, dropping support constraint on favor weighted quadratic penalty, eliminates misbehaviour. With proper choice weight operator, component any minimizer objective function differs least-squares by less than linear combination radius data noise-to-signal ratio.