# Practical cone-beam algorithm

@article{Feldkamp1984PracticalCA, title={Practical cone-beam algorithm}, author={Lee A. Feldkamp and Lloyd Craig Davis and James W. Kress}, journal={Journal of The Optical Society of America A-optics Image Science and Vision}, year={1984}, volume={1}, pages={612-619} }

A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a…

## 5,945 Citations

### A cone-beam tomography algorithm for orthogonal circle-and-line orbit.

- PhysicsPhysics in medicine and biology
- 1992

A cone- beam algorithm which provides a practical implementation of B D Smith's cone-beam inversion formula is presented, in the form of a convolution-back projection, and requires a pre-filtering procedure.

### Filter design in three-dimensional cone beam tomography: circular scanning geometry

- Mathematics
- 2003

The aim of this paper is to present a general approach to derive inversion formulae for 3D cone beam tomography. Starting from the approximate inverse we derive reconstruction kernels using the…

### Filter design in three-dimensional cone beam tomography: circular scanning geometry

- Mathematics
- 2003

The aim of this paper is to present a general approach to derive inversion formulae for 3D cone beam tomography. Starting from the approximate inverse we derive reconstruction kernels using the…

### Cone-beam reconstruction by backprojection and filtering.

- Mathematics, PhysicsJournal of the Optical Society of America. A, Optics, image science, and vision
- 2000

A new analytical method for tomographic image reconstruction from cone-beam projections acquired on the source orbits lying on a cylinder is presented, and a formula for an approximate shift-invariant inverse filter is derived.

### Derivation and analysis of a new reconstruction formula from cone-beam projections

- Mathematics
- 1996

Abstract. A new method to compute the first derivative of 3-D Radon transform is given for cone-beam data taken from any orbit. Smith [11] and Grangeat [5] even derived cone-beam inversion formulas…

### Computing Reconstruction Kernels for Circular 3-D Cone Beam Tomography

- MathematicsIEEE Transactions on Medical Imaging
- 2008

The mathematical model and a general strategy, the so-called approximate inverse, for deriving both exact and numerical inversion formulas are introduced and a 2-D shift-invariant filter for circular-orbit cone-beam imaging is derived.

### A Two-step Fan-beam Backprojection Slice Theorem

- Mathematics
- 2018

In this work, we propose a theoretical formulation for the tomographic linear fan-beam backprojection having low computational cost. The proposed formula is obtained from a recent backprojection…

### A fast and efficient method for sequential cone-beam tomography

- Mathematics2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149)
- 2000

A fast and efficient approximative reconstruction method for sequential cone-beam tomography is presented that is based on the tent-FDK method and can handle axially truncated projections.

### Derivation and analysis of a filtered backprojection algorithm for cone beam projection data.

- MathematicsIEEE transactions on medical imaging
- 1991

An approximate reconstruction formula is developed and shown to be essentially equivalent to the practical cone-beam algorithm of L.A. Feldkamp et al. (1984) and the resulting spatially varying point spread function is examined.

### A filtered-backprojection cone-beam algorithm for general orbits with implementation details for the two-orthogonal-circles orbit

- Physics, Mathematics1993 IEEE Conference Record Nuclear Science Symposium and Medical Imaging Conference
- 1993

A new cone-beam reconstruction algorithm for general orbits is presented. The algorithm is derived from an exact analytical inversion formula and has the form of a shift-variant filtered…

## References

SHOWING 1-10 OF 17 REFERENCES

### Convolutional Reconstruction from Cone-Beam Projection Data

- Physics, MathematicsIEEE Transactions on Nuclear Science
- 1979

A convolutional formula is obtained for the direct reconstruction of a three-dimensional structure function from cone-beam projection measurements. The cone apex is assumed to move on a circle to…

### AN INVERSION FORMULA FOR CONE-BEAM RECONSTRUCTION*

- Mathematics, Physics
- 1983

An analytic inversion formula allowing the reconstruction of a three-dimensional object from x-ray cone-beams is given. The formula is valid for the case where the source of the beams describes a…

### Direct Three-Dimensional Image Reconstruction from Divergent Rays

- MathematicsIEEE Transactions on Nuclear Science
- 1979

The solutions to the image reconstruction problem, in two and three dimensions, for both parallel and divergent ray geometries, are presented within a general linear reconstruction framework. It is…

### Iterative Three-Dimensional Reconstruction from Twin-Cone Beam Projections

- Physics, MathematicsIEEE Transactions on Nuclear Science
- 1978

The results indicate that the ART-reconstruction from twin-cone beam projections can be achieved without blurring artefacts.

### Reconstruction of 3-D objects from cone beam projections

- MathematicsProceedings of the IEEE
- 1978

A true three-dimensional reconstruction (TTR) algorithm which is applicable to a cone beam with 4π detection geometry is introduced. The TTR differs from conventional slice by slice 3-D…

### The Fourier reconstruction of a head section

- Physics
- 1974

The authors compare the Fourier algorithm and a search algorithm using a simulated phantom to speed the search algorithm by using fewer interactions leaves decreased resolution in the region just inside the skull which could mask a subdural hematoma.

### Ectomography-A New Radiographic Reconstruction Method-II. Computer Simulated Experiments

- MathematicsIEEE Transactions on Biomedical Engineering
- 1980

In a special radiographic process, ectomography, an image of a slice is produced by simple summation of a set of specially filtered component images, of which each represents one of at least 60…

### Ectomography-A New Radiographic Reconstruction Method-I. Theory and Error Estimates

- Materials ScienceIEEE Transactions on Biomedical Engineering
- 1980

Radiographic technology has advanced considerably during the last years with the advent of reconstruction techniques allowing visualization of slices through the body. In spite of the advantage of…