München 2009 – scientific programme

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ST: Fachverband Strahlen- und Medizinphysik

ST 11: Novel X-Ray Tomographic Imaging

ST 11.2: Talk

Thursday, March 12, 2009, 14:20–14:40, A021

Tomographic reconstruction with a priori geometrical information — •Mattia Fredrigo, Andreas Wenger, and Christoph Hoeschen — Helmholtz Zentrum München, Institut für Strahlenschutz, Neuherberg

Computed tomography (CT) is critically important in medical diagnostics, but it is also the main source of human exposure to ionizing radiation. To reduce this risk factor, contemporary CT research strives to improve the trade-off between radiation dose and image quality, for instance by developing sensitive detectors (less radiation power), efficient irradiation geometries (less scattering and exposure) or optimized reconstruction algorithms (denoising, anti-aliasing, etc.). Examples of reconstruction strategies are direct algebraic inversion (ART), filtered Fourier back-projection (FBP) or orthogonal polynomial expansion on the disk (OPED).

A new reconstruction algorithm for CT is proposed, integrating a priori geometrical information in order to reconstruct images from an under-sampled Radon data set, thereby directly reducing the required radiation exposure for a given image resolution. The integrated geometrical information could be partial and provided by a less invasive but possibly otherwise limited diagnostic tool, like magnetic resonance imaging. The proposed algorithm extends the algebraic inversion strategy (where x is the reconstructed image, b is the Radon spectrum and A is the projection matrix) by means of a penalization term, consisting of a gaussian smoothing kernel S truncated at some given edges (the a priori geometrical information):

where β is a penalization parameter and I is the identity matrix. The numerical inversion is performed iteratively by the method of the conjugate gradient. An homogeneous and isotropic smoothing kernel penalization allows undersampling by imposing soft continuity conditions, generally blurring the image. By truncating the kernel on a given subset of known edges, these can remain sharp during the reconstruction. The available Radon data set information can therefore be more efficiently used to reconstruct the unknown areas. In algebraic terms, the global minimum of the penalized inversion is closer to the original image. We developed and implemented such an algorithm and investigated reconstructions from limited number of projections e.g. of the Shepp-Logan-phantom. Method and results will be shown.