Local basis-function approach to computed tomography

Hanson, Kenneth M.; Wecksung, G.W.

doi:10.1364/ao.24.004028

Cited by 94 publications

(42 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, our voxel-driven perspective projection algorithm is considerably more accurate than the one described by Westover [23]. Our ray-driven algorithm, on the other hand, is a 3D extension of the 2D algorithm proposed by Hanson and Wecksung [10].…”

Section: Introductionmentioning

confidence: 90%

“…Since accurate integration requires many sampling points, this is very time consuming. A better way that allows a more efficient and more accurate evaluation of the ray integral was proposed by a number of authors [10] [14][15] [23]. It consists of reordering the ray integral so that each voxel's contribution to the integral can be viewed isolated from the other voxels.…”

Section: Preliminaries and Previous Workmentioning

confidence: 99%

“…We can then map all voxel footprints to the screen, scaled by the voxel value, where they accumulate into a projection image, as is done in the splatting approach of Westover [23]. Alternatively, one can use rays to intersect the lookup tables in volume space, again scale the indexed value by the voxel value, and accumulate the density integrals ray by ray [10][14] [15]. The former approach we call voxel-driven splatting, which produces an image or an image region at a time and makes only sense in conjunction with an image-based correction algorithm, such as SART.…”

Section: Preliminaries and Previous Workmentioning

confidence: 99%

See 2 more Smart Citations

Fast and accurate projection algorithm for 3D cone-beam reconstruction with the Algebraic Reconstruction Technique (ART)

Mueller

Yagel²,

Wheller

1998

SPIE Proceedings

View full text Add to dashboard Cite

The prime motivation of this work is to devise a projection algorithm that makes the Algebraic Reconstruction Technique (ART) and related methods more efficient for routine clinical use without compromising their accuracy. While we focus mostly on a fast implementation of ART-type methods in the context of 3D cone-beam reconstruction, most of the material presented here is also applicable to speed up 2D slice reconstruction from fan-beam data.In this paper, we utilize the concepts of the splatting algorithm, which is a well known and very efficient voxel-driven projection technique for parallel projection, and devise an extension for perspective cone-beam projection that is considerably more accurate than previously outlined extensions. Since this new voxel-driven splatting algorithm must make great sacrifices with regards to computational speed, we describe a new 3D ray-driven projector that uses similar concepts than the voxel-driven projector but is considerably faster, and, at the same time, also more accurate. We conclude that with the proposed fast projection algorithm the computational cost of cone-beam ART can be reduced significantly with the added benefit of slight gains in accuracy. A further conclusion of our studies is that for parallel-beam reconstruction, on the other hand, a simple voxel-driven splatting algorithm provides for more efficient projection.

show abstract

Section: Introductionmentioning

confidence: 90%

Section: Preliminaries and Previous Workmentioning

confidence: 99%

Section: Preliminaries and Previous Workmentioning

confidence: 99%

See 1 more Smart Citation

Fast and accurate projection algorithm for 3D cone-beam reconstruction with the Algebraic Reconstruction Technique (ART)

Mueller

Yagel²,

Wheller

1998

SPIE Proceedings

View full text Add to dashboard Cite

show abstract

“…In limiting the resolution, it is desirable to avoid the Examples of various methods of displaying coarsely sampled projection data (60 views, 32 samples /view), taken from Ref. 50, in order of improving visual usefulness: a) contour plot of projection data, b) isometric projection (or 3 -D relief) of same, c) continuous tone (gray -scale) display of same, d) 32 x 32 pixel reconstruction of original scene from the data using square pixels, e) the same reconstruction displayed using bilinear interpolation, f) 32 x 32 grid reconstruction from the same data using B-spline basis functions, and g) image of original object.…”

Section: The Displayed Imagementioning

confidence: 99%

Image Processing: Mathematics, Engineering, Or Art?

Hanson

1985

SPIE Proceedings

Self Cite

View full text Add to dashboard Cite

From the strict mathematical viewpoint, it is impossible to fully achieve the goal of digital image processing, which is to determine an unknown function of two dimensions from a finite number of discrete measurements linearly related to it. However, the necessity to display image data in a form that is visually useful to an observer supersedes such mathematically correct admonitions. Engineering defines the technological limits of what kind of image processing can be done and how the resulting image can be displayed. The appeal and usefulness of the final image to the human eye pertains to aesthetics.Effective image processing necessitates unification of mathematical theory, practical implementation, and artistic display. Figure 1 shows the basic elements of any imaging scheme. The fundamental purpose of imaging is to convey information about the object to the observer, usually a human being. The measurements obtained at the input stage of imaging can assume various forms. They might consist of spatially separated samples of the luminosity of visibly detectable light, as in light photography. IntroductionOr, as is most often the case in medical imaging, the measurements might be of nonvisual quantities, such as x -ray intensity, the strength or time delay of sonic pulses, or the intensity of radiation being emitted by the object. In the newest form of medical imaging, that of nuclear magnetic resonance, the measurements involve a complex arrangement of magnetic and radiofrequency fields and the quantities being imaged are closely related to the density of the nuclei under study in combination with the relaxation times of the nuclear spins.Between the measurements and the display of the final image, some form of processing takes place.In photography or film -based radiography, the processing consists in film development. We will be more concerned here with digital image processing in which the measurements are manipulated by a digital computer.In order to emphasize the unity of the processing and display stages of imaging, we will assume the term "image processing" comprises both.It is typically desired that the observer synthesize the displayed information in order to draw a conclusion (make a diagnosis) about the object. Thus, the available information should be presented to the observer in such a way that he can most readily interpret it. Presently, the most efficient way to present the human observer with a vast amount of correlated information is through his visual sense. Thus, we will assume the end product of image processing is a visual image or picture. It is the purpose of imaging to provide an observer, usually a human being, information about the object under study. The information content is fundamentally limited by the measurements taken. Image processing, which naturally includes both the processing and display stages of the imaging chain, should convey as much of that information as possible in a form useful to that observer. From the strict mathematical viewpoint, it is impossible to ful...

show abstract

“…From then on, many research results on theoretical analysis and actual applications of CT were obtained [1][2][3][4][5][6][7][8][9][10][11]. With the continuous development of CT, more and more research branches are formed.…”

Section: Introductionmentioning

confidence: 99%

Relaxation Factor Optimization for Common Iterative Algorithms in Optical Computed Tomography

Jiang

Zhang

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Optical computed tomography technique has been widely used in pathological diagnosis and clinical medicine. For most of optical computed tomography algorithms, the relaxation factor plays a very important role in the quality of the reconstruction image. In this paper, the optimal relaxation factors of the ART, MART, and SART algorithms for bimodal asymmetrical and three-peak asymmetrical tested images are analyzed and discussed. Furthermore, the reconstructions with Gaussian noise are also considered to evaluate the antinoise ability of the above three algorithms. The numerical simulation results show that the reconstruction errors and the optimal relaxation factors are greatly influenced by the Gaussian noise. This research will provide a good theoretical foundation and reference value for pathological diagnosis, especially for ophthalmic, dental, breast, cardiovascular, and gastrointestinal diseases.

show abstract

Local basis-function approach to computed tomography

Cited by 94 publications

References 28 publications

Fast and accurate projection algorithm for 3D cone-beam reconstruction with the Algebraic Reconstruction Technique (ART)

Fast and accurate projection algorithm for 3D cone-beam reconstruction with the Algebraic Reconstruction Technique (ART)

Image Processing: Mathematics, Engineering, Or Art?

Relaxation Factor Optimization for Common Iterative Algorithms in Optical Computed Tomography

Contact Info

Product

Resources

About