@MASTERSTHESIS\{IMM2004-03044,
    author       = "M. Vinther",
    title        = "Inverse problems in acoustic reflectometry",
    year         = "2004",
    keywords     = "Acoustic reflectometry, inverse problems, regularization, devonvolution, inverse scattering, loss modeling",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    note         = "This project has been completed in collaboration with Oticon. The project can be acquired by contacting Per Christian Hansen, pch@imm.dtu.dk",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/3044-full.html",
    abstract     = "We examine acoustic reflectometry as a method for determining the inner cross section of a cavity. The cavity is modeled as a cylindrical tube with varying cross section area. A method for making practical measurements using a speaker, a microphone and sampling hardware is described, and algorithms for computing the cross section area from the measurements are derived. Both a lossless and a lossy model is derived, and issues in creating and using the models are studied.

The cross section area is computed using an inverse scattering algorithm
working on the impulse response of the cavity. Estimating the impulse response from our experi­men­tal data proves to be an ill-posed problem, i.e. with a solution that is very sensitive to per­tu­r­bations in the input. The performance of different regularization methods applied to this problem is investigated with respect to quality of the result and computational complexity.

Determining the cross section area is also a potentially ill-posed problem, and stability of the suggested methods is examined.

In Danish:

Akustisk reflektometri bliver unders{\o}gt som metode til at bestemme det indre
tv{\ae}rsnit af en r{\o}rformet kavitet. I den forbindelse beskrives en mulig metode til at foretage de faktiske m{\aa}linger v.h.a. lydgiver, mikrofon og samplinghardware, og algoritmer til at beregne tv{\ae}r­snitsareal ud fra m{\aa}ledata udledes. Kaviteten modelleres b{\aa}de som et tabsfrit og et tabsgivende r{\o}r, og problematikker omkring modellering af tab studeres.

Tv{\ae}rsnitsarealet viser sig at kunne beregnes simplest ud fra kavitetens impulssvar, og at bestemme impulssvaret kr{\ae}ver l{\o}sning af et regulariseringsproblem. Derfor bliver for­skel­lige regu­lariserings­metoder unders{\o}gt med hensyn til beregningseffektivitet og deres evne til at frembringe tilfresstillinde resultater.

B{\aa}de bestemmelse af tv{\ae}rsnitsareal og impulssvar er s{\aa}kaldte inverse problemer, hvortil l{\o}sningen potentielt er meget f{\o}lsom overfor forstyrrelser i m{\aa}ledata."
}