An analytical algorithm for skew-slit collimator SPECT with uniform attenuation correction

Abstract

To replace the conventional pinhole (normal cone-beam) collimator, a novel skew-slit collimator was previously proposed and a Novikov-type algorithm developed to reconstruct images using the skew-slit geometry. The goal of this paper is to develop a reconstruction algorithm that has better noise control than the Novikov-type algorithm. The new algorithm is able to compensate for uniform attenuation, and computer simulation results show that reconstructed images are less noisy.

Figure 1

A skew-slit collimator consists of two tungsten plates. Each plate contains a slit. The two slits are orthogonal to each other.

Figure 2

Each slit consists of focal points of the projection rays.

Figure 3

Illustration of a multi-skew-slit system.

Figure 4

Illustration of the skew-slit backprojection geometry.

Figure 5

Illustration of the boundary factor D.

Figure 6

Reconstructed images. The first row shows the true phantom, the second row shows the images reconstructed from the pinhole system, the third row shows the images reconstructed from the skew-slit system and the last row shows the images reconstructed from the multi-skew-slit system. The left column shows the transaxial central-slice (i.e. the orbit plane) images. The middle and right columns show the two orthogonal central-slice images perpendicular to the trajectory.

Figure 7

Reconstructed images. The first row shows the true phantom, the second row shows the images reconstructed from the pinhole system, the third row shows the images reconstructed from the skew-slit system and the fourth row shows the images reconstructed from the multi-skew-slit system. The left column shows the central-slice images parallel to the trajectory. The middle and right columns show the two orthogonal central-slice images perpendicular to the trajectory.

Figure 8

Images reconstructed from noise-free projections. The images of the first row were reconstructed from skew-slit noise-free projections by the Novikov-type algorithm in Huang and Zeng (2006), and the images of the second row were reconstructed from the multi-skew-slit noise-free projection by the Novikov-type algorithm. The images of the first column are the z = 0 slice, the images of the second column and the third column are the x = 0 and y = 0 slices, respectively.

Figure 9

Images reconstructed from noisy skew-slit projections. The images in the first row were reconstructed by the Novikov-type algorithm in Huang and Zeng (2006) from skew-slit noisy projections, and the images in the second row were reconstructed by the proposed algorithm from the same skew-slit noisy projections. The images of the first column are the z = 0 slice, the images of the second column and the third column are the x = 0 and y = 0 slices, respectively. The white circles show the sampled region for standard deviation calculation.

Figure 10

Images reconstructed from noisy multi-skew-slit projections. The images in the first row were reconstructed by the Novikov-type algorithm in Huang and Zeng (2006) from multi-skew-slit noisy projections, and the images in the second row were reconstructed by the proposed algorithm from the same multi-skew-slit noisy projections. The images of the first column are the z = 0 slice, the images of the second column and the third column are the x = 0 and y = 0 slices, respectively. The white circles show the sampled region for standard deviation calculation.