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13 February 2007 Parametric image reconstruction using the discrete cosine transform for optical tomograhy
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It is well know that the inverse problem in optical tomography is highly ill-posed. The image reconstruction process is often unstable and non-unique, because the number of the boundary measurements data is far fewer than the number of the unknown parameters (optical properties) to be reconstructed. To overcome this problem one can either increase the number of measurement data (e.g. multi-spectral or multi-frequency methods), or reduce the number of unknows (e.g. using prior structural information from other imaging modalities). In this paper, we introduce a novel approach for reducing the unknown parameters in the reconstruction process. The discrete cosine transform (DCT), which has long been used in image compression, is here employed to parameterize the reconstructed image. In general, only a few DCT coefficient are needed to describe the main features in an image, and the number of unknowns in the image reconstruction process can be drastically reduced. Numerical as well as experimental examples are shown that illustrate the performance of the new code.
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Xuejun Gu, Kui Ren, James Masciotti, and Andreas H. Hielscher "Parametric image reconstruction using the discrete cosine transform for optical tomograhy", Proc. SPIE 6434, Optical Tomography and Spectroscopy of Tissue VII, 64342B (13 February 2007);

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