Sparse View CT Image Reconstruction Based on Total Variation and Wavelet Frame Regularization

Abstract

The sparse view problem of image reconstruction encountered in computed tomography (CT) is an important research issue due to its considerable potential in lowering radiation dose. Among the researches, the total variation (TV) method is especially effective in sparse view CT reconstruction for its good ability to preserve sharp edges and suppress noise. However, TV-based methods often produce undesired staircase artifacts in smooth regions of the reconstructed images since the reconstructed problem is usually ill-posed and TV regularization favors piecewise constant functions. Moreover, the image can be accurately approximated by sparse coefficients under a proper wavelet tight frame, which has good capability of sparsely estimating the piecewise smooth functions and the quality of reconstructed image can be improved by the sparse prior information. To deal with sparse view CT reconstruction problem, a minimization hybrid reconstruction model that incorporates TV with the wavelet frame has been proposed, which is to use the TV-norm of the low-frequency wavelet frame coefficients and the $\ell _{0} $ -norm of the high-frequency wavelet frame coefficients to eliminate staircase effect while maintaining sharp edges, simultaneously provide enough regularization in smooth regions. In addition, considering that the two regularization terms produce more parameters, an alternating direction method of multipliers (ADMM) algorithm has been applied to solve the minimization problem by iteratively minimization separately. Finally, compared with several iterative reconstruction methods, the experimental results demonstrate the competitiveness of the proposed method in terms of preserving edges, suppressing staircase artifacts and denoising.