Keywords: parallel image reconstruction, decomposition of and segmentation and registration of modulated image sequences

Information: Project INVERSE is primarily devoted to mathematical image processing, motivated by problems which must be solved in Projects MRI and HEART, and this project plays also a supporting role for parameter estimation and optimal measurement problems which must be solved in projects MRI, HEART and NFI. For the dynamic examination goals in Project MRI, techniques for parallel image reconstruction as well as tissue site tracking and volume determination are required. For the heart anatomy modeling goals in Project HEART, techniques for anatomy reconstruction from histological imaging are required.

These requirements present significant new challenges in image reconstruction, segmentation and registration, and the central theoretical theme among these challenges is that the image processing tasks must be performed simultaneously with multiplicative and additive decompositions of images and image sequences. The required decomposition is multiplicative when images are to be separated into a product of native data and an external modulation, where the modulation can be smooth in the case of varying magnetic resonance imaging coil sensitivities or non-smooth in the case of the sudden appearance of contrast agent or staining artifact in an image sequence. The required decomposition is additive when image sequences are to be separated into moving and non-moving, or rigid and non-rigid parts, which can then be registered and interpolated separately and by means which will be more accurate and more rapid than without decomposition. In cooperation with Projects MRI, HEART and NFI, engineering approaches will be compared synergistically with the variational approaches proposed in INVERSE. With FREELEVEL, MGINV and FEMBEM experience with pre-dual and total variation formulations, multigrid techniques, higher-order Tikhonov regularization, Mumford-Shah segmentation and generalized rigid image registration and interpolation will be utilized.