Artifact Reduction Based On Frequency Domain Optimization For Image Reconstruction From Sparse Projection

X-Ray examination causes more damage on human health with the increase of the amount of X-ray irradiation. For prevention, there should not be x-ray examination unless necessary. Image reconstruction from sparse samples of X-ray computed tomography (CT) would reduce X-ray dose delivered as well as accelerating scanning speed. There would be more artifacts for the reason of sparse projection data. The need for exact image reconstruction in the situation grows with the increasing importance of CT imaging for the difficulty of image reconstruction of sparse projection.However, conventional tomography technology, such as filtered back-projection (FBP) algorithm, will lead to stronger artifacts in reconstruction of tomographic images as the number of projections decreased. The artifacts seriously limit the clinical application of image reconstruction of sparse projection since diagnosis and radiotherapy treatment planning is affected. Researches for image reconstruction algorithm are done and applied for the image reconstruction. Algorithms based on iterative method, such as algebraic reconstruction technique (ART), cost too much time and space although there were good results. Fourier transform algorithm transforms the projection data into the frequency spectrum base on Fourier Central Slice theorem. There are shortcomings that data gridding from polar coordinate to Cartesian coordinate results in error and poor reconstruction.In the frequency spectrum of reconstructed image using conventional FBP algorithm, there are various signal-to-noise ratios (SNRs). Data along the line at the angle of projections have more powerful amplitude than the others, which means there are high SNRs at these places since the energy of noise spreads equally. We reconstruct the image using the high-SNR frequency data in order to remove the artifacts. Lots of algorithm has been developed for frequency data acquisition method of radial imaging, such as conventional gridding algorithm. Iterative next-neighbor regridding or INNG algorithm, import rescaled matrices to improve reconstruction from non-uniformly sampled k-space data. In comparison with conventional gridding focus on improving the calculation of density compensation functions (DCFs), INNG is simple, efficient and accurate, and effective for profile distortions caused by insufficient projection data.Images formed by taking the magnitude of its gradient could be approximately sparse. Exact image reconstruction could be realized by solving a convex optimization problem with the objective function to minimize the l1-norm of the gradient image, or the total variation (TV) of the image. Minimizing the TV of the image estimate can be accomplished in use of the gradient descent method. Using INNG algorithm or TV algorithm obtains better images, but still undesired.We designed a combined scheme based on frequency domain optimization for exact image reconstruction of sparse projection data. Here are the steps of the algorithm: high SNR data is sampled from frequency spectrum, and then processed by using the INNG algorithm combined with TV gradient descent method. As results in the computer simulations indicate, the proposed new approach significantly improves the quality of image reconstructed and effective for profile distortion restricted and oscillations removing, and also makes good performance in the situation of noisy data.