Limited view angle tomographic image reconstruction via total variation minimization

In tomosynthesis, cone-beam projection data are acquired from a few of view angles, which are not sufficient for an exact reconstruction of an image object using state-of-the-art image reconstruction algorithms. In the case of parallel-beam projections, the well-known projection-slice theorem may be utilized to transform the parallel-beam projections into the Fourier space of an image object. Due to the limited range of view angles, the available projection data can only populate a portion of Fourier space. Moreover, the angular sampling rate of the populated portion of the Fourier space may not satisfy the Nyquist criterion. Thus, reconstructed images using direct Fourier inversion contain severe streaking and distortion artifacts. In this paper, we present a novel image reconstruction method via minimizing the total variation (TV) of the reconstructed image for limited view angle X-ray computed tomography. Specifically, the missing data points in Fourier space, due to either the limited range or undersampling of view angles, are iteratively filled using the following two constraint conditions: (1) the total variation of the reconstructed image is minimized and (2) reconstructed image maintains fidelity to the sampled data in the Fourier space. Using analytical phantoms, numerical simulations were conducted to validate the new image reconstruction method. Images are compared with two other image reconstruction methods in terms of image artifact level and noise properties. Numerical results demonstrated that the new image reconstruction algorithm is superior to direct Fourier inversion reconstruction algorithm and the projection onto convex sets (POCS) image reconstruction algorithm.