Contributions of Work Sample Clauses

Contributions of Work. ‌ For different noise distributions, model (1.1) can be transformed into various formats and the methods used to compute solutions are diversified. If we assume that we only have one energy window, then the matrix equation (1.1) is reduced to a nonlinear system of the form y = exp −AW CT s + η, (1.2) where y is the vector of projected data, s collects the information of energy spectrum and η represents the noise vector. For this problem, we transform it into a nonlinear optimization problem that involves both equality and inequality constraints. In order to keep the second order derivative positive semi-definite, we propose a modified Hessian. In addition to the modified Hessian, a problem-specific nonlinear interior- point trust region method is implemented to solve this problem. Moreover, total variation regularization is applied to stabilize the solutions. Both for full CT and limited angle cases, we can obtain images of high quality with this method. If we take the assumption of multiple energy windows and each energy window can only detect a specific range of energy, then the basic model is the same as (1.1). Under the constraint of nonnegative weights, we can build a nonlinear optimization problem as