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Yayın Solution of inverse source problem in thermoacoustic imaging(Işık Üniversitesi, 2022-06-14) Elmas, Demet; Uzun, Banu; Işık Üniversitesi, Lisansüstü Eğitim Enstitüsü, Matematik Doktora ProgramıThis study aims to investigate and explore accurate analytical inverse solutions of thermoacoustic wave equation involved in microwave induced thermoacoustic imaging of breast. Using boundary conditions, we aimed to find more realistic solutions. For cross-sectional two-dimensional thermoacoustic imaging of breast, we explored solution of the wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section. To obtain the forward and inverse solutions of the thermoacoustic wave equation, we derived the Green’s function involving Bessel and Hankel functions by employing the geometrical and acoustic parameters (densities and velocities) of layered media together with temporal initial condition, radiation conditions and continuity conditions on boundaries of layers. The image reconstruction based on this approach involves the layers parameters as the a priori information which can be estimated from the acquired thermoacoustic data. To test and compare our layered solution with conventional solution based on homogeneous medium assumption, we performed simulations using numerical test phantoms consisting of sources distributed in the layered structure. After then, we derived more general integral solution for thermoacoustic wave equation in frequency domain for an arbitrary convex domain in R³.Yayın Cross-sectional thermoacoustic imaging using multi-layer cylindrical media(IEEE, 2017-11-10) Elmas, Demet; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, MustafaFor cross-sectional two-dimensional thermoacustic imaging of breast and brain, we explored solution of the wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section. To obtain the forward and inverse solutions of the thermoacoustic wave equation, we derived the Green's function involving Bessel and Hankel functions by employing the geometrical and acoustic parameters (densities and velocities) of layered media together with temporal initial condition, radiation conditions and continuity conditions on the layers' boundaries. The image reconstruction based on this approach involves the layer parameters as the apriori information which can be estimated from the acquired thermoacoustic data. To test and compare our layered solution with conventional solution based on homogeneous medium assumption, we performed simulations using numerical test phantoms consisting of sources distributed in the layered structure.Yayın Çok katmanlı silindirik yapılar için termoakustik dalga denkleminin ters çözümü(IEEE, 2017-06-27) Elmas, Demet; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, MustafaTermoakustik görüntüleme, elektromanyetik enerji uyarımı ile ultrason dalgaları oluşumunu sağlayan yeni bir yöntemdir. Bu sistemin görüntüleme işlemi termoakustik dalga denkleminin ters çözümüne dayanmaktadır. Ters çözümde görüntülenecek dokunun homojen yapıda olduğu varsayımı, görüntü kalitesinin azalmasına neden olur. Bu çalışmada, meme ve beyinin görüntülemesinde uygulanabilecek üç boyutlu eş merkezli silindirik çok katmanlı yapılar için termoakustik dalga denkleminin analitik ters çözümü elde edilmiştir. Çözümü sayısal olarak test etmek için, noktasal kaynaklar içeren üç katmanlı fantom kullanılarak numerik simulasyonlar elde edilmiştir.
