Preserving Time Structures While Denoising a Dynamical Image
In restoration or denoising of a movie, the classical procedures often do not take into account the full information provided by the movie. These procedures are either applied spatially “image per image” or locally on some neighborhood combining both closeness in one image and closeness in time. The local information is then combined homogeneously in order to realize the treatment. There is one type of movie where both approaches fail to provide a relevant treatment. Such a movie, called dynamical image, represents the same scene along the time with only variations, not in the positions of the objects in the scene but, in their gray levels, colors or contrasts. Hence, at each point of the image, one observes some regular temporal dynamics. This is the typical output using Dynamic Contrast Enhanced Computed Tomography (DCE-CT) or Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) where at each spatial location (called voxel) of the image a time series is recorded.
In such a case, in order to preserve the full temporal information in the image, a proper denoising procedure should be based on averaging over spatial neighborhoods, but using the full dynamics of all pixels (or voxels) within the neighborhood. It is thus necessary to search homogeneous spatial neighborhoods with respect to the full dynamical information.
We introduce a new algorithm which meets these requirements. It is based on two main tools: a multiple hypothesis testing for the zero mean of a vector and an adaptive construction of homogeneous neighborhoods. For both tools, results of mathematical statistics ensure the quality of the global procedure. Illustrations from medical image sequences show a very good practical performance.
This work was supported in 2008 by a grant “Bonus Qualité Recherche” from the University Paris Descartes for the project “Cancer Angiogénèse et Outils Mathématiques”.
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