Few-view single photon emission computed tomography (SPECT) reconstruction based on a blurred piecewise constant object model

Abstract

A sparsity-exploiting algorithm intended for few-view single photon emission computed tomography (SPECT) reconstruction is proposed and characterized. The algorithm models the object as piecewise constant subject to a blurring operation. To validate that the algorithm closely approximates the true object in the noiseless case, projection data were generated from an object assuming this model and using the system matrix. Monte Carlo simulations were performed to provide more realistic data of a phantom with varying smoothness across the field of view and a cardiac phantom. Reconstructions were performed across a sweep of two primary design parameters. The results demonstrate that the algorithm recovers the object in a noiseless simulation case. While the algorithm assumes a specific blurring model, the results suggest that the algorithm may provide high reconstruction accuracy even when the object does not match the assumed blurring model. Generally, increased values of the blurring parameter and total variation weighting parameters reduced streaking artifacts, while decreasing spatial resolution. The proposed algorithm demonstrated higher correlation with respect to the true phantom compared to maximum-likelihood expectation maximization (MLEM) reconstructions. Images reconstructed with the proposed algorithm demonstrated reduced streaking artifacts when reconstructing from few views compared to MLEM. The proposed algorithm introduced patchy artifacts in some reconstructed images, depending on the noise level and the selected algorithm parameters. Overall, the results demonstrate preliminary feasibility of a sparsity-exploiting reconstruction algorithm which may be beneficial for few-view SPECT.

Figure 1

Intermediate piecewise constant object, f_true, (left) and the ground-truth object, u_true, obtained by blurring f_true with r_true = 0.75 pixels (right). u_true was the phantom used in the inverse crime simulations.

Figure 2

Images reconstructed from 9 views of noiseless inverse crime data using the proposed algorithm with varying values of r and γ.

Figure 3

Plots depicting the CC over the range of studied r and γ parameters of images reconstructed from noiseless inverse crime data from 128 views (a) and 9 views (b).

Figure 4

Intermediate images f and the number of meaningful sparsity coefficients reconstructed from128 and 9 noiseless inverse crime data using γ = 0.0001.

Figure 5

Images reconstructed from 9 views of noisy data using the proposed algorithm with varying values of r and γ. For these images, the projection data were generated by the system matrix.

Figure 6

Plots depicting the CC over the range of studied r and γ parameters of images reconstructed from noisy data from 128 views (a) and 9 views (b). For these images, the projection data were generated by the system matrix.

Figure 7

Images reconstructed from noisy projections using the proposed algorithm and MLEM for varying sampling cases. For these images, the projection data were generated by the system matrix.

Figure 8

Voxelized phantom used in the GATE studies. The phantom contains contrast elements of varying shape and size as described in Table 2.

Figure 9

Diagram of Simulated SPECT system. The contrast-element phantom used in this study fills the FOV seen by all three pinholes.

Figure 10

Images reconstructed from 60 views of GATE data simulated for 200 seconds using the proposed algorithm with varying values of r and γ.

Figure 11

Plots depicting the CC over the range of studied r and γ parameters of images reconstructed from GATE data simulated for 200 seconds, using 60 views (a) and 9 views (b).

Figure 12

Images reconstructed from 9 views of GATE data simulated for 200 seconds using the proposed algorithm with varying values of r and γ.

Figure 13

Reconstructions of GATE data simulated for 200s over different numbers of angles using the proposed algorithm and MLEM.

Figure 14

Images reconstructed from 9 views of GATE data simulated for 30 seconds using the proposed algorithm with varying values of r and γ.

Figure 15

Plot depicting the CC over the range of studied r and γ parameters of images reconstructed from GATE data simulated for 9 views over 30 seconds.

Figure 16

Images reconstructed using the proposed algorithm and MLEM from GATE data simulated with the same time per view for different numbers of views.

Figure 17

Voxelized phantom adapted from XCAT phantom used in this study.

Figure 18

Images reconstructed from 60 views, 15 views and 9 views using the proposed algorithm and MLEM. Data were generated from GATE simulation of a cardiac phantom. MLEM reconstructions are presented as a reference. As in previous sections, the MLEM stopping iteration was selected as that with the highest CC value.