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We study the inverse boundary value problem for the wave equation using thesingle-layer potential operator as the data. We assume that the data havefrequency content in a bounded interval. We prove how to choose classes ofnonsmooth coefficient functions so that optimization formulations of inversewave problems satisfy the prerequisites for application of steepest descent andNewton-type iterative methods.

Iterative reconstruction of the wavespeed for the wave equation with bounded frequency boundary data