A variational framework for low-dose sinogram restoration

Abstract

Pre-processing the noisy sinogram before reconstruction is an effective and efficient way to solve the low-dose X-ray Computed Tomography (CT) problem. The objective of this paper is to develop a low-dose CT image reconstruction method based on statistical sonogram smoothing approach. The proposed method is casted into a variational framework and the solution of the method is based on minimisation of energy functional. The solution of the method consists of two terms viz. data fidelity term and a regularisation term. The data fidelity term is obtained by minimising the negative log likelihood of the signal dependent Gaussian probability distribution which depicts the noise distribution in low dose X-ray CT. The second term i.e. regularisation term is a non-linear CONvolutional Virtual Electric Field Anisotropic Diffusion (CONVEF-AD) based filter which is an extension of Perona-Malik (P-M) anisotropic diffusion filter. The main task of regularisation function is to address the issue of ill-posedness of the solution for the first term. The proposed method is capable of dealing with both signal dependent and signal independent Gaussian noise i.e. mixed noise. For experimentation purpose, two different sinograms, generated from test phantom images are used. The performance of the proposed method is compared with that of existing methods. The obtained results show that the proposed method outperforms many recent approaches and is capable of removing the mixed noise in low dose X-ray CT.