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

• Published in: IEEE transactions on medical imaging 2000-08, Vol.19 (8), p.773-786
• Main Authors: La Riviere, P.J., Xiaochuan Pan
• Format: Article
• Language: English
• Subjects: Algorithms; Anisotropy; Biological and medical sciences; Computational efficiency; Filtering; Filters; Humans; Image Processing, Computer-Assisted - methods; Image Processing, Computer-Assisted - statistics & numerical data; Image quality; Image reconstruction; Image resolution; Imaging systems; Investigative techniques, diagnostic techniques (general aspects); Iterative algorithms; Least squares approximations; Least squares methods; Likelihood Functions; Mathematical models; Mathematical transformations; Medical sciences; Miscellaneous. Technology; Models, Statistical; Noise; Optical transfer function; Phantoms, Imaging - statistics & numerical data; Poisson Distribution; Positron emission tomography; Radiodiagnosis. Nmr imagery. Nmr spectrometry; Regression Analysis; Reproducibility of Results; Smoothing methods; Statistics; Statistics, Nonparametric; Studies; Tomography; Tomography, Emission-Computed - methods; Tomography, Emission-Computed - statistics & numerical data; Tomography, Emission-Computed, Single-Photon - methods; Tomography, Emission-Computed, Single-Photon - statistics & numerical data
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/42.876303

The authors develop and investigate an approach to tomographic image reconstruction in which nonparametric regression using a roughness-penalized Poisson likelihood objective function is used to smooth each projection independently prior to reconstruction by unapodized filtered backprojection (FBP). As an added generalization, the roughness penalty is expressed in terms of a monotonic transform, known as the link function, of the projections. The approach is compared to shift-invariant projection filtering through the use of a Hanning window as well as to a related nonparametric regression approach that makes use of an objective function based on weighted least squares (WLS) rather than the Poisson likelihood. The approach is found to lead to improvements in resolution-noise tradeoffs over the Hanning filter as well as over the WLS approach. The authors also investigate the resolution and noise effects of three different link functions: the identity, square root, and logarithm links. The choice of link function is found to influence the resolution uniformity and isotropy properties of the reconstructed images. In particular, in the case of an idealized imaging system with intrinsically uniform and isotropic resolution, the choice of a square root link function yields the desirable outcome of essentially uniform and isotropic resolution in reconstructed images, with noise performance still superior to that of the Hanning filter as well as that of the WLS approach.