Haomin Zhou

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  An Orthogonal Solution and Kernel Correction Algorithm for Inverse Source Problems with Applications in Fluorescence Tomography
  Haomin Zhou

  We present a new approach to solve the inverse source problem arising in Fluorescence Tomography (FT). In general, the solution is non-unique and the problem is severely ill-posed. It poses tremendous challenges in image reconstructions. In practice, the most widely used methods are based on Tikhonov-type regularizations, which minimize a cost function consisting of a regularization term and a data fitting term. We propose an alternative method, which overcomes the major difficulties, namely the non-uniqueness of the solution and noisy data fitting, in two separated steps. First we find a particular solution called orthogonal solution that satisfies the data fitting term. Then we add to it a correction function in the kernel space so that the final solution fulfills the regularization and other physical requirements, such as positivity. Moreover, there is no parameter needed to balance the data fitting and regularization terms. In addition, we use an efficient basis to represent the source function to form a hybrid strategy using spectral methods and finite element methods in the algorithm. The resulting algorithm can drastically improve the computation speed over the existing methods. And it is also robust against noise and can greatly improve the image resolutions. This is a joint work with Shui-Nee Chow (Math), Ke Yin (Math) and Ali Behrooz (ECE) from Georgia Tech.