Nonlinear Filter Combined Regularization of Compressed Sensing for CT Image Reconstruction

This chapter presents a framework of nonlinear filter-based compressed sensing (CS) applied on sparse view CT image reconstruction. The conventional algorithms of quadratic-form regularization have been recognized that they fail to take the discontinuities of images into account. They may lead to over smoothed of object boundaries or fine structures in the reconstructed images. The proposed method considers sequential changes of all the local pixels in a designed window. A kind of nonlinear filter, which is median filter, bilateral filter, or non-local weighted means filter, was embedded in the CS framework, respectively. The image reconstruction problem can be treated as a cost function minimization problem. The proposed cost function consists of data fidelity term and penalty term. The penalty term, in which the nonlinear filter works, was designed and tested in ℓ0 norm, ℓ1 norm, and ℓ2 norm. Proximal splitting theory was used for constructing iterative reconstruction methods. Furthermore, we carried out calculation acceleration by constructing row-action structure. In this chapter, we applied the new method to practical medial CT images (dental, chest, and cranial images), and it showed a superior effect in image smoothing, object boundary extracting, and texture preserving. Appropriate adjustment of nonlinear filter parameters is a little complicated, and we will promote the automatic parameter setting or reducing parameter numbers in our future work.