CT image reconstruction from partial angular measurements via compressed sensing

Computed Tomograhpy (CT) is a technology that takes projection data along a trajectory and reconstructs an image of the objects. But it exposes patients to significant radiation. Therefore, lower radiation dose has been constantly pursued. The amount of radiation dose is a function of the number of projections. However, in traditional reconstruction algorithms, for example, filtered back projection (FBP) method, the number of projections must satisfy the Shannon/Nyquist sampling theorem so as to avoid streaking artifacts. In this paper, we apply compressed sensing for CT reconstruction. The algorithm minimizes the ℓ₁ of the wavelet transform coefficient and total variation of the image. It employs FBP to calculate the intermediate results of derivative of the object function in each compressed sensing iteration. Our simulation experiments show that this method can reconstruct CT images from substantially fewer number of projections than the requirement of Shannon/Nyquist limit. Hence the associated radiation dose can be reduced without noticeable aliasing artifacts and streaking artifacts.