Ultrasound modulated bioluminescence tomography (UMBLT) is a technique for imaging the 3D distribution of biological objects such as tumors by using a bioluminescent source as a biomedical indicator. It uses bioluminescence tomography (BLT) with a series of perturbations caused by acoustic vibrations. UMBLT outperforms BLT in terms of spatial resolution. The current UMBLT algorithm in the transport regime requires measurement at every boundary point in all directions, and reconstruction is computationally expensive. In Chapter 2, we will first introduce the UMBLT model in both the diffusive and transport regimes, and then formulate the image reconstruction problem as an inverse source problem using internal data. Second, we present an improved UMBLT algorithm for isotropic sources in the transport regime. Third, we generalize an existing UMBLT algorithm in the diffusive regime to the partial data case and quantify the error caused by uncertainties in the prescribed optical coefficients.The inverse boundary value problem (IBVP) of wave equation aims to recover medium distribution via boundary measurement of wave propagation. Using an important identity that connects boundary data and internal wave states, one can recover the medium's interior structure by selecting suitable boundary sources. In Chapter 3, we will first introduce the IBVP and the key identity. Second, we present a direct wave speed reconstruction algorithm with vanished wave potential. Third, we apply linearization on IBVPs to derive algorithms with nonvanishing parameters for both wave speed and wave potential reconstruction.
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