# 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… Expand

#### 132 Citations

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

- Computer Science
- Proceedings 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. Expand

Image reconstruction from linograms: implementation and evaluation.

- Mathematics, Medicine
- IEEE 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. Expand

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

- Computer Science
- 1995 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. Expand

CT Algorithms With Linograms

- Mathematics
- [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… Expand

An Improved Form of Linogram Algorithm for Image Reconstruction

- Computer Science
- IEEE 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. Expand

Tomographic Image Formation Techniques

- Mathematics
- 2002

Computerized tomography is the process of reconstructing the interiors of objects from collected data based on transmitted or emitted radiation. This article explains the nature of the reconstruction… Expand

The linogram method for image reconstruction from projections applied to fan-beam projection data

- Mathematics
- IEEE Conference on Nuclear Science Symposium and Medical Imaging
- 1992

The linogram method is compared to the fan-beam filtered backprojection method. Fan-beam filtered projection data are assumed. It is shown that the image quality is comparable for the two methods.… Expand

Image reconstruction of diffraction tomography using linograms

- Computer Science
- 1998 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. Expand

Three-dimensional Linogram Reconstruction: Application To Magnetic Resonance Imaging

- Mathematics
- [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… Expand

A dual approach to linogram imaging for MRI

- Computer Science, Medicine
- Magnetic 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. Expand

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Image reconstruction from linograms: implementation and evaluation.

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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. Expand

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