Mathematical Methods in Biomedical Imaging

Biomedical imaging is a rapidly growing field to provide a state-of-the-art tool for preclinical biomedical research and clinical applications, in view of its ability to noninvasively reveal subtle structural variations of biological tissues and visualize in vivo physiological and pathological processes at the cellular and molecular levels. Mathematical methods are involved with imaging theories, models, and reconstruction algorithms in biomedical imaging. X-ray computed tomog-raphy (CT) was a successful application of mathematical method in medical imaging. The CT mathematical model can be reduced to a Radon transform. The inverse transform of Radon transform is invented by Radon in 1917. Magnetic resonance imaging (MRI) is a versatile medical imaging modality. MRI can provide more diagnostic information than any of the existing imaging techniques. It does not involve the use of ionizing radiation, hence free from associated harmful effects. Inverse Fast Fourier Transform (IFFT) is a standard method of image reconstruction in MRI from uniformly sampled K-space data. From nonuniform K-space data, iterative algorithms can improve image quality of image reconstruction for MRI. In the optical molecular imaging, the radiative transport equation (RTE) is the fundamental equation to describe photon propagation in biological tissues. The forward solution predicts photon propagation in the optical molecular imaging. The inverse solution can reconstruct molecular probe distribution in a small animal for providing unique insights into disease pathogenesis, drug development, and responses of therapy. The solutions for RTE usually involve analytical methods, Monte Carlo (MC) method, diffusion approximation (DA) method, simplified spherical harmonics method, and some numerical methods. In this special issue, each paper was reviewed by at least two reviewers and revised according to review comments. This special issue covered most of common biomedical imaging models and various image processing methods, such as registration, segmentation, and so forth, were involved. For Positron Emission Tomography (PET) imaging model, two attenuation correction methods based on X-rays CT (CTAC method) and segmentation of emission images (SE-AC method) were simulated with Monte Carlo method and compared. For synchrotron Micro-CT imaging model, a semiautomatic segmentation algorithm for extracting the complete structure of acini has been proposed. For ultra-sound imaging model, a common carotid artery segmen-tation scheme based on active shape model can get better result and promote the translation of carotid 3D US to clinical care for the monitoring of the atherosclerotic disease progression and regression. For MRI model, a mesh-deformation constraints based image registration algorithm was carefully investigated. Also the …