Abstract: A method and apparatus is provided to iteratively reconstruct a PET image for emission data using separable quadratic surrogates (SQS). The quadratic surrogates include a Poisson likelihood surrogate that has a curvature that depends on a back-projection of an inverse of mean-background signal. The method can be used with Nesterov acceleration and ordered subsets to achieve quadratic convergence to an image minimizing a Poisson Likelihood objective function that includes a regularizer that penalizes roughness in the reconstructed image.

Abstract: An apparatus and method of denoising a dynamic image is provided. The dynamic image can represent a time-series of snapshot images. The dynamic image is transformed, using a sparsifying transformation, into an aggregate image and a series of transform-domain images. The transform-domain images represent kinetic information of the dynamic images (i.e., differences between the snapshots), and the aggregate image represents static information (i.e., features and structure common among the snapshots). The transform-domain images, which can be approximated using a sparse approximation method, are denoised. The denoised transform-domain images are recombined with the aggregate image using an inverse sparsifying transformation to generate a denoised dynamic image. The transform-domain images can be denoised using at least one of a principal component analysis method and a K-SVD method.