Adaptive Super-resolution Medical Image Reconstruction Algorithm

At present super-resolution reconstruction in the military, astronomy, remote sensing, it is also extensive scope of application in the medical field, such as positron emission imaging (Positron Emission Tomography, PET), magnetic resonance imaging (Magnetic Resonance Imaging, MRI), etc. PET is able to represent heart and brain metabolism and functions on molecule level by imaging techniques, and has shown great performance in oncology, cardiopathy, neurology and new medicine studies. But positron emission tomography is an ill-posed inverse problem because the observed projection data are contaminated by noise due to low count rate and physical effects. Traditional method often reconstructs noisy images of low quality, super-resolution methods can be used to improve PET image quality.Image super resolution is the inverse process of image degradation, which is referred to as generating a high-resolution image from one or several low-resolution images. A low-resolution image can be considered as the degraded version of the high-resolution image and the degradations include warping, blurring and down-sampling. Obviously image super-resolution is an ill-conditioned problem. The ill-posed problem could be normally solved by regulation parameter which contains the priori information of the images. The choice of the regulation parameter is very important, which does not only decide the rate of the convergence but also impact the quality of the reconstruction image. Many methods have been proposed to overcome the ill-posed problem in the past twenty years. Many outstanding theories have been proposed in the past 10 years, especially the MG Kang etc propose the parameters of linear regularization method, and then a series of linear regularization algorithms come out. However, the ill-posed problem is nonlinear regularization problems. Consequently a series of nonlinear regularization are proposed in the paper.The nonlinear adaptive regularizationⅠ: The regularization of the adaptive function is proposed by WF.Chen and M. Chen in 2006, which improves the image quality while reduces the amount of computation. According to WF.Chen and M. Chen, H. He and LP Kondi the relevant theoretical foundation, a novel nonlinear adaptive regularization function is proposed. The convexity of the cost function is analyzed experimentally. Based on the convex of the cost function, we get the adaptive step size by the mathematical theory. Consequently, the spatial resolution of the image and the rate of convergence are significantly improved. Optical images are used to test the proposed method. The results show that our algorithm is very effective.The nonlinear adaptive regularizationⅡ: according to H. He and LP Kondi in 2006 reference and RC Hardie, K.J Barnard, and EE Armstrong in 1997 reference. An adaptive linear slope algorithm based on the regularization parameter (RP) is proposed. This algorithm can adaptively optimize the cost function and reduce the suppression of high frequency component of PET image by adaptively updating linear slope of the RP. The proposed method is performed on simulated PET image sequence. The results of the experiment indicate that the proposed algorithm outperforms conventional approaches in the spatial resolution.The nonlinear adaptive regularizationⅢ: In order to obtain high resolution MR images, gradient magnetic field is required and the signal-to-noise will be reduced due to the decrease in voxel size with traditional scan. Based E.S. Lee and M.G Kang algorithm, the adaptive of super resolution MR Image reconstruction, which includes the images prior information is proposed. Usually, it is difficult to prove the convexity of the cost function, when a nonlinear regularization is adopted. Most of time, experimental means is the only way to prove the convexity of the cost function. It is can be proved in the proposed algorithm and ensures that the cost function has a global minimum. As shown from the results obtained in the phantom imaging, the proposed super resolution technique can improve the resolution of MR image. The new algorithm is superior to other algorithms by experimental comparative analysis.