written by John Bardsley

(unless otherwise noted)

(Last Modified 1/2012) Supervised Classification and Spatial Smoothing This collection of codes performs supervised classification of multi-banded imagery, from remote sensing to standard RGB images. It was written by myself, Marylesa Howard, Chris Gotshalk, and Mark Lorang, for the accompanying paper.

(Last Modified, 9/2010) A Nonnegatively Constrained, Convex Programming Algorithm: This is the code that was used in the papers "A Nonnnegatively Constrained Convex Programming Method for Image Reconstruction", "Total Variation-Penalized Poisson Likelihood Estimation for Ill-Posed Problems", "Tikhonov Regularized Poisson Likelihood Estimation: Theoretical Justification and a Computational Method", "An Efficient Computational Method for Total Variation with Poisson Negative-Log Likelihood", "An Analysis of Regularization by Diffusion for Ill-Posed Poisson Likelihood Estimation," "An Iterative Method for Edge-Preserving MAP Estimation when Data-Noise is Poisson", "Regularization Parameter Selection Methods for Ill-Posed Poisson Maximum Likelihood Estimation". At this point you can choose Tikhonov, total variation regularization, and diffusion regularization. Regularization parameter selection methods for the Poisson negative-log likelihood are also now available. The main algorithm is for nonnegatively constrained, regularized Poisson likelihood estimation. A number of other methods are also implemented. These include the GPCG algorithm of More' and Toreldo for large-scale bound constrained quadratic minimization, the EM algorithm, the projected gradient method, the projected Newton method and the lagged diffusivity fixed point iteration. There is a "Readme" file to guide you in the use of the codes. Only astronomical imaging examples are considered in these codes; see below for medical imaging implementation.

(Last modified 11/2012) MAP estimation for PET and SPECT imaging. This code implements Poisson MAP estimation in the case of PET and SPECT. Regularization is quadratic (prior is Guassian), but edge preserving. Regularization parameter selection is also implemented if the user wants. These codes were used in the paper "Hierarchical Regularization for Edge-Preserving Reconstruction of PET Images", with Daniela Calvetti and Erkki Somersalo, Inverse Problems, 26(3), 2010, 035010.

(Last modified in 9/2010) WMRNSD for medical imaging examples. The medical imaging examples are computed tomography, positron emission tomography, and single photon emission computed tomography. The relative reference is: "Applications of a Nonnegatively Constrained Iterative Method with Statistically Based Stopping Rules to CT, PET, and SPECT Imaging," Electronic Transactions in Numerical Analysis, 38, 2011, pp. 34-43.