Iterative CT reconstruction based on ADMM using shearlet sparse regularization

The total variation (TV) method favors solutions with the piece-wise constant assumption of the desired image from sparse-view sampling, for example, simple geometric images with flat intensity. When the phantoms become more complex and contain complicated textures, for example, high-resolution phantom and lung CT images, the images reconstructed by TV regularization may lose their contrast and fine structures. One of the optimally sparse transforms for images, the shearlet transform, has C² without discontinuities on C² curves, giving excellent sensitive directional information as compared with other wavelet transform approaches. Here, we developed a Shearlet-Sparse Regularization (SSR) algorithm solved with the Alternating Direction Method of Multipliers (ADMM) to overcome this limitation. With the strengthened characteristics of SSR, we performed one simulation experiment and two real experiments using a NeuViz 64 X-ray CT scanning system to measure the performance and properties of proposed algorithm. The results demonstrate that the SSR method exhibits the advantage of providing high-quality directional information and contrast as compared with TV.