Decomposition of radon projections into stackgrams for filtering, extrapolation, and alignment of sinogram data

Abstract

In computed tomography, information about inner structures of an object (or a patient) is obtained indirectly by numerically reconstructing an image of the object from its measured projections. The measured Radon projections are represented as a sinogram matrix, which can be regarded as a digital image. The sinogram image consists of different mixed and summed sinusoidal curves. Signals along these sinusoids or trajectories contribute to pixel values of the reconstructed image. The reconstructed image can represent, for example, the tracer distribution in the body as in positron emission tomography (PET).

Due to the low signal to noise ratio in measured sinograms in emission tomography, starting point for the thesis has been to develop a procedure to improve the reconstructed image quality from a novel point of view. In the thesis, we present a novel decomposition for the signals along the sinusoidal trajectories of the sinogram. This decomposition, or the stackgram approach, allows processing separately the sinusoidal trajectory signals. In the stackgram representation, the signals can be processed without interfering with the crossing trajectories. This new stackgram approach can be regarded as an intermediate form of the sinogram and reconstructed image representations. A mathematical transformation from the sinogram data into the stackgrams is simple and invertible, and has been introduced in the thesis. In addition, the new stackgram approach is employed for three different applications of the sinogram data.

A proper noise reduction is a relevant issue especially in emission tomography; therefore the first discussed application is data filtering employing the stackgram representation for noise reduction of the sinograms. According to our experimental studies, filtering of the stackgram data does not introduce geometrical distortions in the reconstructed images, and the noise structure of the images is visually not disturbing. These suggest that the stackgram filtering approach can provide a potential alternative to a common sinogram filtering procedure (denoted as radial filtering).

In addition to filtering, we have successfully employed the stackgrams for extrapolation of incomplete sinogram data for limited angle tomography in the thesis. In limited angle tomography the full range of projection views is not available as in the normal case, but it can be numerically estimated for image reconstruction.

The third application presented in the thesis is alignment of the tomographic data. Motion of the object or the patient as well as motion of the organs during the scan cause blurring and artifacts in the reconstructed images. To avoid the artifacts, the scans can be divided into short time frames. The different frames are then numerically aligned for a reference frame, in order to compensate the motion. For the task like this, the proposed stackgram based data driven alignment algorithm is fully automatic, simple, and it is suited for alignment of the data having small changes in spatial positions or structures. This kind of an automated data driven alignment technique for the sinogram data is desired especially in modern emission tomographs.