A constrained, total-variation minimization algorithm for low-intensity x-ray CT

Purpose: The authors developed an iterative image-reconstruction algorithm for application to low-intensity computed tomography projection data, which is based on constrained, total-variation (TV) minimization. The algorithm design focuses on recovering structure on length scales comparable to a detector bin width. Methods: Recovering the resolution on the scale of a detector bin requires that pixel size be much smaller than the bin width. The resulting image array contains many more pixels than data, and this undersampling is overcome with a combination of Fourier upsampling of each projection and the use of constrained, TV minimization, as suggested by compressive sensing. The presented pseudocode for solving constrained, TV minimization is designed to yield an accurate solution to this optimization problem within 100 iterations. Results: The proposed image-reconstruction algorithm is applied to a low-intensity scan of a rabbit with a thin wire to test the resolution. The proposed algorithm is compared to filtered backprojection (FBP). Conclusions: The algorithm may have some advantage over FBP in that the resulting noise level is lowered at equivalent contrast levels of the wire.