Fast fan/parallel beam CS-based low-dose CT reconstruction

Low dose X-ray Computed Tomography (CT) is clinically desired to reduce the risk of cancer caused by X-ray radiation. Compressed Sensing (CS), which allows images to be formed from incomplete data, enables large dose reduction to be achieved. Though this remains to be clinically unrealized due to excessive computation times. In this paper we demonstrate a fast, complete CS-based ℓ₂-TV minimizing CT reconstruction method applicable to both parallel and fan beam geometries to recover high quality images from highly undersampled (thus low-dose) data. We apply the fast pseudo-polar Fourier algorithm and the Central Slice Theorem to reduce the computation time of CS recovery. On a typical desktop computer, we are able to reconstruct a 512×512 CT image in approximately 30 seconds: a clinically-significant speedup compared to the many hours required by previous CS methods.