Comparison of TVcDM and DDcTV algorithms in image reconstruction

ABSTRACT The total variation (TV) minimization algorithms is a classical representative of the optimization algorithms and have been widely used for their simpleness, robustness, expandability and their potential of accurately reconstructing images from sparse data or noisy data. The commonly used constrained TV (cTV) program is the data-divergence constrained TV (DDcTV) minimization. The other recently proposed cTV program is the TV constrained data-divergence minimization (TVcDM). In the work, we compare the two programs the convergence rate and the reconstruction accuracy via the sparse-view projection set and the noisy projection set in the context of CT. Further, we compare their reconstruction accuracy via real data in electron paramagnetic resonance imaging (EPRI). The studies show that TVcDM has much faster convergence rate relative to DDcTV and that TVcDM may achieve higher accuracy in most cases no matter in sparse-view projections CT reconstructions or in noisy projections CT reconstructions or in EPRI sparse reconstructions. From a comprehensive perspective, TVcDM has superior convergence and accurate reconstruction performance relative to DDcTV and should be recommended in the application of TV reconstruction algorithms. The knowledge and insights gained in the work may be extended to the performance analysis of other optimization-based reconstruction algorithms.