A new Mumford–Shah total variation minimization based model for sparse-view x-ray computed tomography image reconstruction

Total variation (TV) minimization for the sparse-view x-ray computer tomography (CT) reconstruction has been widely explored to reduce radiation dose. However, owing to the piecewise constant assumption, CT images reconstructed by TV minimization-based algorithms often suffer from image edge over-smoothness. To address this issue, an improved sparse-view CT reconstruction algorithm is proposed in this work by incorporating a Mumford–Shah total variation (MSTV) model into the penalized weighted least-squares (PWLS) scheme, termed as “PWLS-MSTV”. The MSTV model is derived by coupling TV minimization and Mumford–Shah segmentation, to achieve good edge-preserving performance during image denoising. To evaluate the performance of the present PWLS-MSTV algorithm, both qualitative and quantitative studies were conducted by using a digital XCAT phantom and a physical phantom. Experimental results show that the present PWLS-MSTV algorithm has noticeable gains over the existing algorithms in terms of noise reduction, contrast-to-ratio measure and edge-preservation.