<title>Penalized-likelihood image reconstruction for emission tomography using higher-order convex-nonquadratic priors</title>

Abstract

Penalized-likelihood method using Bayesian smoothing priors have formed the core of the development of reconstruction algorithms for emission tomography. In particular, there has been considerable interest in edge-preserving prior models, which are associated with smoothing penalty functions that are nonquadratic functions of nearby pixel differences. Our early work used a higher-order nonconvex prior that imposed piecewise smoothness on the first derivative of the solution to achieve result superior to those obtained using a conventional nonconvex prior that imposed piecewise smoothness on the zeroth derivative. In spite of several advantages of the higher-order model - the weak plate, its use in routine applications has been hindered by several factors, such as the computational expenses to the on convexity of its penalty function and the difficult in the selection of hyperparameters involved in the model. We note that, by choosing a penalty function which is nonquadratic but is still convex, both the problem of nonconvexity involved in some nonquadratic priors and the over smoothness of edge region sin quadratic priors may be avoided. In this paper, we use a class of 2D smoothing splines with first and second spatial derivatives applied to edge-preserving ability, we use the quantitation of bias/variance and total squared error over noise trials using the Monte Carlo method. Our experimental results show that linear combination of low and high orders of spatial derivatives applied to convex-nonquadratic penalty functions improves the reconstruction in terms of total squared error.