3-D Object Reconstruction in Emission and Transmission Tomography with Limited Angular Input

Tam, K. C.; Perez‐Mendez, V.; Macdonald, B.

doi:10.1109/tns.1979.4330539

Cited by 35 publications

(13 citation statements)

References 6 publications

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“…An iterative algorithm for reconstructing the object from limited-angle projection data was developed in earlier works [4,5). The algorithm is sketched in Figure 11.…”

Section: Limited-angle Image Reconstructionmentioning

confidence: 99%

Digital Tomography Incorporating a Priori Information

Tam¹,

Thomas²

1990

Review of Progress in Quantitative Nondestructive Evaluation

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The technique of tomography has long been used in radiography and in nuclear medicine to sharpen images of objects on the tomographic plane and to blur images of objects on the off-planes. The method is illustrated in Figure 1. Suppose one is interested in examining the plane Tin the object. The x-ray source and the film are moved parallel to each other in the opposite directions with the plane of interest as the fulcrum. This is achieved by choosing the velocity v1 of the x-ray source and the velocity v 2 of the film such that the ratio v1/v2 is equal to difd 2 , where d 1 is the source-to-plane distance, and d 2 is the plane-to-film distance. The objects on the plane of interest are in focus, whereas the objects on the other planes are out of focus and blurred. However, the blurrings could become quite serious in some cases and interfere with the objects of interest.

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“…An iterative algorithm for reconstructing the object from limited-angle projection data was developed in earlier works [4,5). The algorithm is sketched in Figure 11.…”

Section: Limited-angle Image Reconstructionmentioning

confidence: 99%

Digital Tomography Incorporating a Priori Information

Tam¹,

Thomas²

1990

Review of Progress in Quantitative Nondestructive Evaluation

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“…The surface Si2 should be chosen not too close to the origin so that reconstructions are not oversmoothed beyond the desirable resolution. As shown in [1,5], one way to recover the components in the missing cone is by means of the iterative scheme shown in Fig. 5.…”

Section: Deconvolution With Iterationsmentioning

confidence: 99%

Limited Angle 3-D Reconstructions from Continuous and Pinhole Projections

Tam

Perez‐Mendez

Macdonald

1980

IEEE Trans. Nucl. Sci.

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The propagation of errors incurred in 3-D reconstructions with limited angular input performed by deconvolution and matrix inversion algorithms is analyzed. The convergence rate and noise properties of an iterative scheme that utilizes the finite extent of the object to recover the missing Fourier components in deconvolution are studied. Methods are developed to stabilize the performance of the reconstruction algorithms in the presence of noise. An analysis is given for the necessary condition for complete reconstruction in imaging situations involving a number of discrete inputs confined to limited angular range.

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“…It has been shown that in such cases the Fourier components of an object that can be measured directly are those outside a cone-shaped region in the Fourier space [1,2]. In principle, all the missing Fourier components can be recovered completely if the object is known to be finite in extent [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…An iteration algorithm has been proposed in our previous papers [1,2] to recover the missing-cone Fourier components of an object distribution. The algorithm is shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

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Limits to Image Reconstruction from Restricted Angular Input

Tam

Perez‐Mendez

1981

IEEE Trans. Nucl. Sci.

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Distortion in an object due to the unavailability of some Fourier components in a cone-shaped region is analyzed. The results throw light on the factors that limit the accuracy in reconstructing objects from limited-angle input in practice. It is also shown that norm-or entropy-relatedreconstruction methods are not expected to improve the fidelity of the reconstructed images; only more a priori knowledge of exact nature on the object can serve this purpose.

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3-D Object Reconstruction in Emission and Transmission Tomography with Limited Angular Input

Cited by 35 publications

References 6 publications

Digital Tomography Incorporating a Priori Information

Digital Tomography Incorporating a Priori Information

Limited Angle 3-D Reconstructions from Continuous and Pinhole Projections

Limits to Image Reconstruction from Restricted Angular Input

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