Compressed sensing (CS) requires undersampled projection data, but CT x-ray tubes cannot be pulsed quickly enough to achieve reduced-view undersampling. We propose an alternative within-view undersampling strategy, named SparseCT, as a practical CS technique to reduce CT radiation dose. SparseCT uses a multi-slit collimator (MSC) to interrupt the x-ray beam, thus acquiring undersampled projection data directly. This study evaluated the feasibility of SparseCT via simulations using a standardized patient dataset. Because the projection data in the dataset are fully sampled, we retrospectively undersample the projection data to simulate SparseCT acquisitions in three steps. First, two photon distributions were simulated, representing the cases with and without the MSC. Second, by comparing the two distributions, detector regions with more than 80% of x-ray blocked by the MSC were identified and the corresponding projection data were not used. Third, noise was inserted into the rest of the projection data to account for the increase in quantum noise due to reduced flux (partial MSC blockage). The undersampled projection data were then reconstructed iteratively using a penalized weighted least squares cost function with the conjugate gradient algorithm. The image reconstruction problem promotes sparsity in the solution and incorporates the undersampling model. Weighting factors were applied to the projection data during the reconstruction to account for the noise variation in the undersampled projection. Compared to images acquired with reduced tube current (provided in the standardized patient dataset), SparseCT undersampling presented less image noise while preserving pathologies and fine structures such as vessels in the reconstructed images.