| Most of today's medical imaging modalities are based on tomography, the process of obtaining slice or volumetric images of the body by way of a computation known as image reconstruction. Tomographic image reconstruction is an ill-posed inverse problem; thus, the results can be greatly affected by noise present in the data. Steps must be taken in the computations to reduce the noise effect and thus improve the quality of the reconstructed images.; The focus of this thesis is the development of new techniques for image reconstruction based on content-adaptive mesh modeling (CAMM) of the image. Specifically, we replace the pixel basis, which is conventionally used to describe images, with a mesh description that is tailored to the specific image.; The CAMM approach involves partitioning of the image domain into a collection of non-overlapping patches, called mesh elements, then describing the intensity over each element through interpolation from the model parameters. The CAMM is content-adaptive, meaning that the mesh is generated so that dense image samples are placed in regions of the image containing high-frequency features while sparse samples are placed in regions containing predominantly low-frequency features.; Approaches based on CAMM have several potential advantages over pixel-based methods: (1) the CAMM provides a natural smoothing effect; (2) the CAMM is a more compact description of the image than a uniform pixel grid, therefore it may require less memory and computation time; (3) since the CAMM reduces the number of parameters to be estimated, making discrete inversion overdetermined, and thus improving image quality; and (4) the CAMM provides a natural framework for estimating motion for reconstruction of moving image sequences.; In this thesis, the basics of the CAMM are presented and later extended to tomographic image reconstruction. It is shown that the use of a CAMM in image reconstruction can achieve good image quality at low computational cost. Further the CAMM is shown to successfully track the heart wall, which exhibits motion, for use in reconstruction and post-reconstruction processing of the image sequence.; In addition, a new method for estimating distinct time-sequence basis functions in an image sequence is presented. This method improves on existing cluster component analysis of image sequences by better modeling their statistical properties. This approach may be useful for new temporal basis function approaches for reconstruction.; Finally, a new method of watermarking, a method of embedding a packet of additional digital data into an image, based on deformable mesh modeling is proposed that is robust to attack by geometrical deformation. |
