6 December 1996 Fast inversion scheme for the linearized problem in optical absorption tomography on objects with radially symmetric boundaries
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Abstract
We present a reconstruction scheme which solves the inverse linear problem in optical absorption tomography for radially symmetric objects. This is a relevant geometry for optical diagnosis in soft tissues, e.g. breast, testis and even head. The algorithm utilizes an invariance property of the linear imaging operator in homogeneously scattering media. The inverse problem is solved in the Fourier space of the angular component leading to a considerable dimension reduction which allows to compute the inverse in a direct way using singular value decomposition. There are two major advantages of this approach. First the inverse operator can be stored in computer memory and the computation of the inverse problem comprises only a few matrix multiplications. This makes the algorithm very fast and suitable for parallel execution. On the other hand we obtain the spectrum of the imaging operator that allows conclusions about reconstruction limits in the presence of noise and gives a termination criterion for image synthesis. To demonstrate the capabilities of this scheme reconstruction results from synthetic and phantom data are presented.
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Uwe Hampel, Uwe Hampel, Richard Freyer, Richard Freyer, "Fast inversion scheme for the linearized problem in optical absorption tomography on objects with radially symmetric boundaries", Proc. SPIE 2925, Photon Propagation in Tissues II, (6 December 1996); doi: 10.1117/12.260854; https://doi.org/10.1117/12.260854
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