Spherically symmetric volume elements with smooth tapering of the values near their boundaries are alternatives to the more conventional voxels for the construction of volume images in the computer. Their use, instead of voxels, introduces additional parameters which enable the user to control the shape of the volume element (blob) and consequently to control the characteristics of the images produced by iterative methods for reconstruction from projection data. For images composed of blobs, efficient algorithms have been designed for the projection and discrete back-projection operations, which are the crucial parts of iterative reconstruction methods. The authors have investigated the relationship between the values of the blob parameters and the properties of images represented by the blobs. Experiments show that using blobs in iterative reconstruction methods leads to substantial improvement in the reconstruction performance, based on visual quality and on quantitative measures, in comparison with the voxel case. The images reconstructed using appropriately chosen blobs are characterized by less image noise for both noiseless data and noisy data, without loss of image resolution.

Practical considerations for 3-D image reconstruction using spherically symmetric volume elements

Three-dimensional computed tomography for optical microscopes

State-of-the-art reconstruction algorithms for medical helical cone-beam Computed Tomography (CT) are of type non-exact Filtered Backprojection (FBP). They are attractive because of their simplicit ...

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Iterative Filtered Backprojection Methods for Helical Cone-Beam CT

We present reconstruction methods for radial magnetic resonance imaging (MRI) data which were spatially encoded using a pair of orthogonal multipolar magnetic fields for in-plane encoding and parallel imaging. It is shown that a direct method exists in addition to iterative reconstruction. Standard direct projection reconstruction algorithms can be combined with a previously developed direct reconstruction for multipolar encoding fields acquired with Cartesian trajectories. The algorithm is simplified by recasting the reconstruction problem into polar coordinates. In this formulation distortion and aliasing become separate effects. Distortion occurs only along the radial direction and aliasing along the azimuthal direction. Moreover, aliased points are equidistantly distributed in this representation, and, consequently, Cartesian SENSE is directly applicable with highly effective unfolding properties for radio-frequency coils arranged with a radial symmetry. The direct and iterative methods are applied to simulated data to analyze basic properties of the algorithms and for the first time also measured in vivo data are presented. The results are compared to linear spatial encoding using a radial trajectory and quadrupolar encoding using a Cartesian trajectory. The direct reconstruction gives good results for fully sampled datasets. Undersampled datasets, however, show star-shaped artifacts, which are significantly reduced with the iterative reconstruction.

Radial Imaging With Multipolar Magnetic Encoding Fields

Contemporary algorithms employed for reconstruction of 3D volumes from helical cone beam projections are so called non-exact algorithms. This means that the reconstructed volumes contain artifacts ...

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Combining analytical and iterative reconstruction in helical cone-beam CT

We discuss a discrete Radon transform in a continuous space in order to establish an analytically exact method to synthesize projections from discretely sampled data. The method shown is based on sampling theory and assumes that an object is band limited. Comparisons with conventional projection methods, namely, linear interpolation and pixel projection, are shown together with a computer simulation.

Shigeru Ohki

Papers

Discrete Radon transform in a continuous space