Nonparametric regression sinogram smoothing using a roughness-penalized Poisson likelihood objective function

We develop and investigate an approach to tomographic image reconstruction in which nonparametric regression using a roughness-penalized Poisson likel ihood objective function is used to smooth each projection independently pr ior to reconstruction by unapodized filtered backprojection (FBP), As an ad ded generalization, the roughness penalty is expressed in terms of a monoto nic transform, known as the link function, of the projections. The approach is compared to shift-invariant projection filtering through the use of a H anning window as well as to a related nonparametric regression approach tha t makes use of an objective function based on weighted least squares (WLS) rather than the Poisson likelihood, The approach is found to lead to improv ements in resolution-noise tradeoffs over the Hanning filter as well as ove r the WLS approach. We also investigate the resolution and noise effects of three different link functions: the identity, square root, and logarithm l inks. The choice of link function is found to influence the resolution unif ormity and isotropy properties of the reconstructed images. In particular, in the case of an idealized imaging system with intrinsically uniform and i sotropic resolution, the choice of a square root link function yields the d esirable outcome of essentially uniform and isotropic resolution in reconst ructed images, with noise performance still superior to that of the Hanning filter as well as that of the WLS approach.