Sparse-view CT Image Reconstruction Using the Logarithmic Barrier Based Interior Point Method

This work aims to develop a logarithmic barrier based interior point method capable of reconstructing CT images using under-sampled sinogram data. Unlike other compressed sensing methods, the proposed method obviates the need of the regularization parameter in the objective function. Feasibility of the algorithm and quality of the reconstructed images were examined. Methods: The sinogram data were simulated through Radon-transforming clinical CT images. The noise was added based on the Poisson and Gaussian models. The basic elements of the proposed method, logarithmic barrier (LB) method, were introduced. The relative Root-Mean-Squared Error (rRMSE) was used to evaluate the image reconstruction accuracy. The noise of the images was assessed using the Peak Signal-to-Noise Ratio (PSNR) and Mean Squared Error (MSE). Results: The PSNR, rRMSE, MSE were compared among fvFBP (full-view Filtered-Backprojection), svFBP (sparse-view Filtered-Backprojection), BB (Barzilai-Borwein), and LB methods for brain, head and neck, lung, prostate, and leg sites. The reconstructed images from svFBP suffered severe streak artifacts. The LB method was capable of reconstructing images of quality comparable to quality of those images obtained from other compressed sensing-based methods such as the BB method. Conclusion: It has been demonstrated that the compressed sensing technique based on the logatirhmic barrier method is capable of recovering satisfactory images from under-sampled projection data. This method obviates the need of the regularization parameter that specifies the relative weight between the data fidelity and total variation terms in the objective function. Insights have been gained as to implementing the proposed method for clinical imaging applications.