We present a fast, cell-centered multigrid solver and apply it to image denoising and nonrigid diffusion based image registration. In both applications real time performance is required in 3D and the multigrid method has to be compared to solvers based on Fast Fourier Transform. The optimization of the underlying variational approach results for image denoising directly in one time step of a parabolic linear heat equation, for image registration a non-linear 2nd order system of partial differential equations is obtained. This system is solved by a fixpoint iteration using a semi-implicit time discretization, where each time step again results in an elliptic linear heat equation. The multigrid implementation comes close to real time performance for medium size medical images in 3D for both applications and is compared to a solver based on Fast Fourier Transform using available libraries. 1

Mathematical methods for time series analysis and digital image processing

Many problems in imaging are actually inverse problems. One reason for this is that conditions and parameters of the physical processes underlying the actual image acquisition are usually not known. Examples for this are the inhomogeneities of the magnet field in magnetic resonance images leading to

Abstract not found

Abstract—The comparison of inter- with intra-ictal SPECT images plays an important role during the diagnosis and treatment of epilepsy patients. Although there is already commercial software available to address this problem using complex clinical workflows, this article describes a different way of looking at this issue. During the examination various issues arise from differing tracer concentrations, patient movement between the acquisitions at different times and also the lack of morphological information. The goal of the presented work is therefore to present an approach that is on the one hand easy to use for the physician and on the other hand both reliable and robust enough to cope with the previously mentioned challenges. The proposed algorithm introduces methods that have already been applied successfully in digital subtraction angiography (DSA). The work comprises of several steps for the intensity normalization, image registration, difference imaging and the incorporation of an MR image for the spatial localization. As a result, information is provided about differences within the cerebral blood flow (CBF) and active brain areas between the intra- and inter-ictal states. Very new to the field of SPECT brain imaging is the application of non-rigid registration techniques. This helps to drastically reduce the artifacts within the difference images due to a bias of the standard rigid registration. Acquired results from a collective of 11 patients show that this additional feature helps to further improve the image quality. Index Terms—SPECT, epilepsy, difference, subtraction, rigid registration, nonrigid registration

Many problems in imaging are actually inverse problems. One reason for this is that conditions and parameters of the physical processes underlying the actual image acquisition are usually not known. Examples for this are the inhomogeneities of the magnetic field in magnetic resonance imaging (MRI) leading112 J. F. Acker et al.

Many problems in imaging are actually inverse problems. One reason for this is that conditions and parameters of the physical processes underlying the actual image acquisition are usually not known. Examples for this are the inhomogeneities of the magnet field in magnetic resonance images leading to