Carl Ross Crawford

Two algorithms for the three‐dimensional reconstruction of tomograms

Three-dimensional (3-D) surface reconstructions provide a method to view complex anatomy contained in a set of computed tomography (CT), magnetic resonance imaging (MRI), or single photon emission computed tomography tomograms. Existing methods of 3-D display generate images based on the distance from an imaginary observation point to a patch on the surface and on the surface normal of the patch. We believe that the normalized gradient of the original values in the CT or MRI tomograms provides a better estimate for the surface normal and hence results in higher quality 3-D images. Then two algorithms that generate 3-D surface models are presented. The new methods use polygon and point primitives to interface with computer-aided design equipment. Finally, several 3-D images of both bony and soft tissue show the skull, spine, internal air cavities of the head and abdomen, and the abdominal aorta in detail.

Respiratory compensation in projection imaging using a magnification and displacement model

Respiratory motion during the collection of computed tomography (CT) projections generates structured artifacts and a loss of resolution that can render the scans unusable. This motion is problematic in scans of those patients who cannot suspend respiration, such as the very young or intubated patients. Here, the authors present an algorithm that can be used to reduce motion artifacts in CT scans caused by respiration. An approximate model for the effect of respiration is that the object cross section under interrogation experiences time-varying magnification and displacement along two axes. Using this model an exact filtered backprojection algorithm is derived for the case of parallel projections. The result is extended to generate an approximate reconstruction formula for fan-beam projections. Computer simulations and scans of phantoms on a commercial CT scanner validate the new reconstruction algorithms for parallel and fan-beam projections. Significant reduction in respiratory artifacts is demonstrated clinically when the motion model is satisfied. The method can be applied to projection data used in CT, single photon emission computed tomography (SPECT), positron emission tomography (PET), and magnetic resonance imaging (MRI).

Method and apparatus for coherent imaging system

A method and apparatus for improved digital processing of the analog echo signals in a coherent imaging system is described which simplifies the channel circuitry requirements. The analog echo signals detected with a phased array of transducer elements are first compressed in a non-linear manner then expanded non-linearly with analog-to-digital converter means to provide increased instantaneous dynamic range in the overall system. Representative phased array coherent imaging systems having the improved digital processing means are also disclosed.

Reconstruction Algorithm for Fan Beam with a Displaced Center-of-Rotation

A convolutional backprojection algorithm is derived for a fan beam geometry that has its center-of-rotation displaced from the midline of the fan beam. In single photon emission computed tomography (SPECT), where a transaxial converging collimator is used with a rotating gamma camera, it is difficult to precisely align the collimator so that the mechanical center-of-rotation is colinear with the midline of the fan beam. A displacement of the center-of-rotation can also occur in X-ray CT when the X-ray source is mispositioned. Standard reconstruction algorithms which directly filter and backproject the fan beam data without rebinning into parallel beam geometry have been derived for a geometry having its center-of-rotation at the midline of the fan beam. However, in the case of a misalignment of the center-of-rotation, if these conventional reconstruction algorithms are used to reconstruct the fan beam projections, structured artifacts and a loss of resolution will result. We illustrate these artifacts with simulations and demonstrate how the news algorithm corrects for this misalignment. We also show a method to estimate the parameters of the fan beam geometry including the shift in the center-of-rotation.

Reconstruction for fan beam with an angular dependent displaced center of rotation

A convolutional backprojection algorithm is derived for a fan beam geometry that has an angular-dependent displacement in its center-of-rotation from the midline of the fan beam. In both x-ray computed tomography and single photon emission computed tomography, misalignment can occur when the mechanical center-of-rotation is not colinear with midline of the fan beam. In some cases the shift in the center-of-rotation is constant for every angle, whereas, in other cases it varies with angular position. Standard reconstruction algorithms, which directly filter and backproject the fan beam data without rebinning into parallel beam geometry, have been derived for a geometry having its center-of-rotation at the midline of the fan beam. However, in the case of any misalignment of the center-of-rotation, if these conventional reconstruction algorithms are used to reconstruct the fan beam projections, structured artifacts and a loss of resolution will result. Simulations are performed that illustrate these artifacts and demonstrate how the new algorithm corrects for this misalignment. A method for estimating the parameters of the fan beam geometry, including the angular-dependent shift in the center-of-rotation, is also described.

High Speed Reprojection And Its Applications

Reprojection is the process by which projections are produced from an image such that, if these projections are filtered and backprojected, they yield the original image. Because of the computational expense of reprojection, algorithms that employ this process have never been widely used. A method is presented that enables an unmodified backprojector to be used as a reprojector. Because backprojectors are designed to exploit the parallelism in the backprojection algorithm, the time required to obtain reprojections is significantly reduced. Another method, based on the Fourier Slice Theorem, is presented that enables a general purpose array processor to be used as a high speed reprojector. It is also shown that the parameters of the reprojection algorithm can be adjusted to decrease significantly the time required to perform an application that uses reprojection. Finally, two applications of reprojection in computed tomography are discussed.

Reduction of motion artifacts in computed tomography

The authors report on an analysis of motion artifacts by retrospectively reconstructing partial scan images, scanning moving phantoms, and using computer simulations of the scanner and moving object. The partial scan reconstructions eliminated some artifacts. Phantom and computer simulations substantially reproduced the clinical artifacts and provided insight into the relationships between motion, artifacts and scanner parameters. It is concluded that motion artifacts can be reduced by short scan times combined with gantry synchronization to align the X-ray beam along the axis of any residual motion.<<ETX>>

3-D imaging using normalized gradient shading

Two algorithms called marching cubes and dividing cubes were previously (1987) developed and used for the three-dimensional display of objects contained in CT (computed tomography) and MRI (magnetic resonance imaging) images. A key to these algorithms is that surface normals are derived from the normalized gradient of the original tomographic images. The resulting images have been subjectively judged superior to images generated with the cuberille and ray-casting algorithms. The authors show how the cuberille and ray-casting algorithms can be extended to use the normalized gradient. The image quality attainable using the four existing and the two extended algorithms is demonstrated, and the implementation tradeoffs for the algorithms are discussed.<<ETX>>

3-D Imaging Using Normalized Gradient Shading in CT and MRI

In previous work3-4 two algorithms were developed called Marching Cubes and Dividing Cubes for the three-dimensional display of objects contained in CT and MRI images. A key to these algorithms is that surface normals are derived from the normalized gradient of the original tomographic images. The resulting images have been subjectively judged superior to images generated with the Cuberille and Ray-casting algorithms. This paper shows how the Cuberille and Ray-casting algorithms can be extended to use the normalized gradient. The image quality attainable using the four existing and the two extended algorithms will be demonstrated and the implementation trade-offs for the algorithms will be discussed. We will also show how the display methods can be extended using recursive applications of custom-designed region-growing algorithms. Results will be shown that demonstrate how the modified algorithms have been used to disarticulate bones and to isolate soft tissue structures in CT and MRI.

Iterative Ct Reconstruction Using Reprojection

Reprojection is the process by which projections are produced from an image such that, if these projections are reconstructed, they yield the original image. Because of the computational expense of reprojection, algorithms that employ this process have never been widely used. We present three techniques to speed up reprojection. The methods either exploit hardware already present in commercial CT scanners or the fact that reprojections can be of lower bandwidth than the original projections. We will also show how the reprojections can be used to correct for the presence of metal and for beam hardening artifacts.