Principles of image reconstruction methods

Multidimensional medical imaging in most radiological applications involves three major tasks: (1) raw data acquisition using imaging instrumentation; (2) image reconstruction from the raw data; and (3) image display and processing operations as needed. Image reconstruction in multidimensional space is generally an ill posed problem, where a unique solution representing an ideal reconstruction of the true object from the acquired raw data may not be possible due to limitations on data acquisition. However, using specific filtering operations on the acquired raw data along with appropriate assumptions and constraints in the reconstruction methods, a feasible solution for image reconstruction can be obtained. Radon transform has been most extensively used in image reconstruction from acquired projection data in medical imaging applications such as X-ray computed tomography. Fourier transform is directly applied to the raw data for reconstructing images in medical imaging applications, such as magnetic resonance imaging (MRI) where the raw data is acquired in frequency domain. Statistical estimation and optimization methods often show advantages in obtaining better results in image reconstruction dealing with the ill posed problems of imaging. This chapter describes principles of image reconstruction in multidimensional space from raw data using basic transform and estimation methods.