Non-local total-variation (NLTV) minimization combined with reweighted L1-norm for compressed sensing CT reconstruction

Abstract

The compressed sensing (CS) technique has been employed to reconstruct CT/CBCT images from fewer projections as it is designed to recover a sparse signal from highly under-sampled measurements. Since the CT image itself cannot be sparse, a variety of transforms were developed to make the image sufficiently sparse. The total-variation (TV) transform with local image gradient in L1-norm was adopted in most cases. This approach, however, which utilizes very local information and penalizes the weight at a constant rate regardless of different degrees of spatial gradient, may not produce qualified reconstructed images from noise-contaminated CT projection data. This work presents a new non-local operator of total-variation (NLTV) to overcome the deficits stated above by utilizing a more global search and non-uniform weight penalization in reconstruction. To further improve the reconstructed results, a reweighted L1-norm that approximates the ideal sparse signal recovery of the L0-norm is incorporated into the NLTV reconstruction with additional iterates. This study tested the proposed reconstruction method (reweighted NLTV) from under-sampled projections of 4 objects and 5 experiments (1 digital phantom with low and high noise scenarios, 1 pelvic CT, and 2 CBCT images). We assessed its performance against the conventional TV, NLTV and reweighted TV transforms in the tissue contrast, reconstruction accuracy, and imaging resolution by comparing contrast-noise-ratio (CNR), normalized root-mean square error (nRMSE), and profiles of the reconstructed images. Relative to the conventional NLTV, combining the reweighted L1-norm with NLTV further enhanced the CNRs by 2–4 times and improved reconstruction accuracy. Overall, except for the digital phantom with low noise simulation, our proposed algorithm produced the reconstructed image with the lowest nRMSEs and the highest CNRs for each experiment.