Filtered backprojection inversion of the cone beam transform for a general class of curves

We extend a cone beam transform inversion formula, proposed earlier for helices by one of the authors, to a general class of curves. The inversion formula remains efficient, because filtering is shift-invariant and is performed along a one-parametric family of lines. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much, and do not admit lines which are tangent to C at one point and intersect C at another point. The notions of PI lines and PI segments are generalized, and their properties are studied. The domain U is found, where PI lines are guaranteed to be unique. Results of numerical experiments demonstrate very good image quality

Cardiac Computed Tomography Methods and Systems Using Fast Exact / Quasi Exact Filtered Back Projection Algorithms

The present invention provides systems, methods, and devices for improved computed tomography. More specifically, the present invention includes methods for improved cone-beam computed tomography (CBCT) resolution using improved filtered back projection (FBP) algorithms, which can be used for cardiac tomography and across other tomographic modalities. Embodiments provide methods, systems, and devices for reconstructing an image from projection data provided by a computed tomography scanner using the algorithms disclosed herein to generate an image with improved temporal resolution

Local ROI Reconstruction via Generalized FBP and BPF Algorithms along More Flexible Curves

We study the local region-of-interest (ROI) reconstruction problem, also referred to as the local CT problem. Our scheme includes two steps: (a) the local truncated normal-dose projections are extended to global dataset by combining a few global low-dose projections; (b) the ROI are reconstructed by either the generalized filtered backprojection (FBP) or backprojection-filtration (BPF) algorithms. The simulation results show that both the FBP and BPF algorithms can reconstruct satisfactory results with image quality in the ROI comparable to that of the corresponding global CT reconstruction

Efficient Cone Beam Reconstruction For The Distorted Circle And Line Trajectory

We propose an exact filtered backprojection algorithm for inversion of the cone beam data in the case when the trajectory is composed of a distorted circle and a line segment. The length of the scan is determined by the region of interest , and it is independent of the size of the object. With few geometric restrictions on the curve, we show that we have an exact reconstruction. Numerical experiments demonstrate good image quality

Mathematics and Algorithms in Tomography

This was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis

Mathematical Methods in Tomography

This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century

Mathematics and Algorithms in Tomography

This is the eighth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, sonar, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, vector tomography, and texture analysis