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IDL Demo Library |
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IDL is the industrial-strength processing and visualization environment used by many major equipment medical imaging equipment manufacturers and radiology professionals. This demonstration illustrates the mechanics of reconstructing the cross section of an object, given projections through the object from multiple directions. Many modern medical imaging modalities, including computerized tomography (CT) magnetic resonance imaging (MRI) and positron emission tomography (PET) employ reconstruction to synthesize images from a series of scans acquired at different orientations.
This demonstration begins with the actual cross section of a simulated object, called the phantom. A projection contains M points. There is a total of N projections that have an equal angular distance from each another. The N projections are constructed by summing along lines drawn through the object. Stacking the N projections to form an M column by N row matrix forms a "sinogram" which is shown in the lower left corner. This simulates the actual data that would be acquired by an actual instrument.
From the sinogram, each row (projection) is convolved with the selected filter. Then they are summed (back-projected) into a matrix. The reconstructed image, after all projections have been summed, is shown in the upper right corner. The difference between the reconstructed and the original slices is shown in the lower right corner.
This demonstration is interactive in that the "ray" through the original image corresponding to each point of the sinogram is drawn by clicking the mouse on the sinogram image. Conversely, all points of the sinogram that pass through a given point of the original (phantom) image are illustrated by clicking on that image. Clicking on the error image displays a plot of the horizontal profiles through the original and reconstructed images.
The IDL RADON function is used to compute both the projections and to sum the back-projections.
Operation of this demonstration is quite simple. First select the reconstruction parameters, using the buttons at the lower left, and then press the "Reconstruct" button. After two or more reconstructions have been computed, they may be compared by pressing the "Compare" button.
Select one of the various simulated objects (including Shepp-Logan Phantom, Circles, Squares, or Computerized Tomography scanning slice) from the "Objects" sub-menu.
Select "Reconstruct" to perform the numerical reconstruction and display the images.
Select "Quit" to exit the demo.
Select "Color Palette" to activate a palette chooser and manipulator tool for fine-tuning of the color palette and display contrast.
Select "Redraw" to redraw the images minus the line overlays.
Select "Compare" to display the four most recent reconstructions.
Select "About Reconstruction" to display this help text.
Select the number of views or angles. Note that on small screen monitors, the image size might be smaller than the number of angles and the sinogram views will not show the image in its entirety.
Selects the type of filter (or none) used to convolve each projection before back-projecting.
Select the half-width of the filter convolution kernel. Larger values give better results.
Select either nearest neighbor or linear interpolation. Linear interpolation provides the best results, but takes longest to compute.
Selecting a point in the original image draws a line through the sinogram over the points whose rays are derived from the selected point.
Selecting a point in the sinogram draws the corresponding ray in the Phantom image and the profile of the ray sum (line integral) all parallel rays.
Selecting a point makes a plot showing horizontal profiles through the selected row of the original phantom (solid line), and the reconstructed image (points).
IDL Demo Online Help (October 11, 2006)