New Method On Information Divergence In Medical Tomographic Imaging

Medical tomographic imaging is a kind of non-destructive technology, which can Show the anatomical morphology of the human body clearly and reflect the Physiological and biochemical Process of Pathological changes. So it has been one of the most important tools in medical diagnostic imaging field.The Medical tomographic imaging technology, such as X-CT and E-CT, makes use of a series of Projection data of target from different observation angles to reconstruct tomographic images. The reconstruction algorithms in X-CT and E-CT have the same Mathematical Principle, and can be investigated under the identical mathematical model.However, medical tomographic imaging is an ill-posed inverse problem because of the low counts rate and the low signal to noise ratio of the observed PET and low-dose CT projection data which are contaminated by noise and physical effects. Though needing less computation cost, traditional filter back projection (FBP) method often reconstruct noisy images of low quality. Better expressing system models of physical effects and modeling the statistical Poisson character of the data, the famous maximum likelihood expectation maximization (ML-EM) approach outperforms the FBP method with regard to image quality. However, pure traditional ML-EM approach suffers slow convergence and the reconstructed activity images always start deteriorating to produce "checkerboard effect" as the iteration proceeds. MAP (Maximum A Posteriori) methods, which incorporate MRP prior information of objective isotope density data into the ML-EM algorithm through regularization or prior terms, have been proved theoretically correct and practically effective compared to other methods. Compared to traditional ML-EM algorithm, Bayesian reconstruction shows a better performance in both improving convergence behavior and producing more appealing images.There are usually two terms in the objective function. The first one, also named data fidelity term, models the statistics of projection data. The second one, also named a prior information, regularizes the solution of the data fidelity. Accurate noise modeling is a prerequisite of a statistical iterative reconstruction algorithm. Since the projection data obey compound Poisson distribution in theory that the solutions obtained from the current related algorithm based on poisson or Gaussian distribution model are sub-optimal, then the challenge will be taken into correctness of the modeling of projection data noise model, a divergence, which is a generalization of KL divergence and χ2-divergence, is usually used to measure the difference between probability distributions p(x) and q (x). KL divergence is equivalent to ML model, and χ2-divergence is equivalent to WLS model. So, it is possible to determine the projection data noise model using a divergence. Typically, α divergence can provide more robust and accruate solution with respect to high noise dataThe reasonable regularization term also plays an important role for successful image reconstruction. However, the smoothing QM (Quadratic Membrane) smoothing prior tends to produce an unfavorable over-smoothing effect, and the edge-preserving non-quadratic prior might also bring staircase edge artifact to reconstruction. Recently, compressive sensing (CS) has attracted a significant research interest in recovering high-quality signals or reconstructing high-quality images from fewer measurements. Typically, the CS-based image reconstruction is achieved by total variation (TV) minimization.According to the outstanding performance of a divergence in statistical distribution measure between data sets and edge Preservation characteristic of tatal variation, in this paper we propose a novel total variation (TV) based α-divergence minimization tomographic reconstruction algorithm, which is called as the αD-TV algorithm. The presented αD-TV cost function uses the α-divergence to measure the discrepancy between the measured and the estimated projection data and utilizes the total variation regularization to regularize the consistency of solution. A semi-implicit iteration scheme is first used in the αD-TV algorithm by adapting the subgradient theory; and then an adaptive nonmonotone line search scheme is taken to guarantee the algorithm convergence. The experiments from the simulated phantom data and the real data show that the presented αD-TV algorithm performs better than other classical tomographic reconstruction methods in the noise suppressing and the edge details preserving.