# Linograms in Image Reconstruction from Projections

@article{Edholm1987LinogramsII, title={Linograms in Image Reconstruction from Projections}, author={Paul R. Edholm and Gabor T. Herman}, journal={IEEE Transactions on Medical Imaging}, year={1987}, volume={6}, pages={301-307} }

The notion of a linogram is introduced. It corresponds to the notion of a sinogram in the conventional representation of projection data in image reconstruction. In the sinogram, points which correspond to rays which go through a fixed point in the cross section to be reconstructed all fall on a sinusoidal curve. In the linogram, however, these points fall on a straight line. Thus, backprojection corresponds to integration along straight lines in the linogram. A theorem is proved expressing the…

## 139 Citations

### Linograms in image reconstruction from projections. 1. Back projecting using the Radon transform

- MathematicsProceedings of the Twenty-First Annual Hawaii International Conference on System Sciences, 1988. Vol.IV. Applications Track
- 1988

A theorem is described which expresses the back projection operator in terms of the Radon transform and simple changes of variables and a novel image reconstruction method based on the theorem is introduced.

### Image reconstruction from linograms: implementation and evaluation.

- MathematicsIEEE transactions on medical imaging
- 1988

It is demonstrated that the performance of the algorithm is superior to that of the filter back projection method in computational speed on realistic size problems and is equivalent to filtered backprojection in accuracy of reconstruction.

### 3D-reconstruction using cone-beam backprojection, the Radon transform and linogram techniques

- Mathematics1995 IEEE Nuclear Science Symposium and Medical Imaging Conference Record
- 1995

The paper investigates the application of the linogram technique to an exact cone-beam filtered-backprojection algorithm and demonstrates the image improvement allowed by the use of linograms, as well as an important speed-up of the reconstruction.

### CT Algorithms With Linograms

- Physics[1990] Proceedings of the Twelfth Annual International Conference of the IEEE Engineering in Medicine and Biology Society
- 1990

In this paper two algorithms for linograms are compared. The first algorithm, the Linogram Method (LM), has been described earlier [l-51. The second method, the Direct Fourier Method with linograms…

### An Improved Form of Linogram Algorithm for Image Reconstruction

- Computer ScienceIEEE Transactions on Nuclear Science
- 2008

The theoretical analysis gives the optimal way of implementing the linogram algorithm, leading to savings in computational time and memory space and validated by numerical simulations.

### Image reconstruction of diffraction tomography using linograms

- Mathematics1998 IEEE Ultrasonics Symposium. Proceedings (Cat. No. 98CH36102)
- 1998

It was proved that the speed distribution of an object can be estimated from the image intensity when it is not largely different from that of the surrounding medium.

### Three-dimensional Linogram Reconstruction: Application To Magnetic Resonance Imaging

- Physics[1990] Proceedings of the Twelfth Annual International Conference of the IEEE Engineering in Medicine and Biology Society
- 1990

A novel method of image reconstruction from projections, linogram reconstruction, has previously been described in two dimensions. In this paper, I describe a three-dimensional linogram…

### A dual approach to linogram imaging for MRI

- PhysicsMagnetic resonance in medicine
- 1997

An alternate scheme for linogram image reconstruction, which is more logical from the viewpoint of its applicability to MRI data, is presented here and corresponds directly with the geometry of linogram data collected for MRI, in contrast to the LM reconstruction.

### Analytic and iterative reconstruction algorithms in SPECT.

- MathematicsJournal of nuclear medicine : official publication, Society of Nuclear Medicine
- 2002

A general overview of analytic and iterative methods of reconstruction in SPECT is presented with a special focus on filter backprojection (FBP), conjugate gradient, maximum likelihood expectation maximization, and maximum a posteriori expectation maximizations algorithms.

### Filter calculation for x-ray tomosynthesis reconstruction

- MathematicsPhysics in medicine and biology
- 2012

This paper proposes a new method to design effective filters which are specific for the acquisition geometry and examples from x-ray tomosynthesis are utilized to demonstrate the excellent performance of the proposed method.

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It is demonstrated that the performance of the algorithm is superior to that of the filter back projection method in computational speed on realistic size problems and is equivalent to filtered backprojection in accuracy of reconstruction.

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