Projection Data Smoothing for Low-Dose CT Based on $$\ell _p$$ℓp Regularization

Abstract

Projection data smoothing is a traditional technique for low-dose computed tomography. The projection data can be modeled as a piecewise smooth function. It’s well known that $$\ell _1$$ regularization of the image gradients tries to recover piecewise constant functions, while $$\ell _2$$ regularization recovers smooth functions. This motivates us to propose the $$\ell _p$$ regularization with $$1<p<2$$ for low-dose projection data smoothing. Besides, the non-stationary Gaussian noise model for the projection data is built into the regularization term. The resulting model is then linearized such that the fast split-Bregman algorithm can be applied. Experiments on simulated projection data as well as real data show that $$\ell _p$$ regularization with $$1<p<2$$ could achieve better reconstruction compared to $$\ell _{1}$$ regularization.