MATLAB CODE
written by John Bardsley
(unless otherwise noted)
(Last modified in 1/2007 and written in part by Curt Vogel) Phase Diversity:
This is the code that was used in the paper by Vogel, Gilles, and myself titled "Computational Methods for a Large-Scale Inverse Problem Arising in Atmospheric Optics." It was then added to for use in the paper "An Efficient Estimation Scheme for Phase-Diversity Time Series Data," that I submitted in the fall of 2006. The suite of codes contains implementations of the Limited Memory BFGS algorithm and the Steihaug Newton-CG trust region algorithm for solving a large-scale unconstrained minimization. For postprocessing, the suite contains the nonnegatively constrained methods Modified Residual Norm Steepest Descent (MRNSD), covariance preconditioned MRNSD, and Richardson-Lucy. There are README files to guide you in the use of the codes.
(Last Modified, 1/2007) Adaptive Optics:
This is the code that was used in the papers "Wavefront Reconstruction Methods for Adaptive Optics Systems on Ground-Based Telescopes" and "An Analysis of a Wavefront Reconstruction Problem Arising in Adaptive Optics". The data generation codes were created by Curt Vogel. There are README files to guide you in the use of the codes.
(Last Modified, 2/2007) 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", and "An Efficient Computational Method for Total Variation with Poisson Negative-Log Likelihood". See my publications page for more details. The main algorithm is for nonnegatively constrained, regularized Poisson likelihood estimation. At this point you can choose either Tikhonov or total variation regularization. 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 are README files to guide you in the use of the codes.
(Last Modified, 12/2004) A bound constrained, ellipsoidal trust region implementation of the Levenburg-Marquardt algorithm: In addition
to this algorithm, there is a "classical" implementation of
Levenburg-Marquardt. Examples using both real data from a vibrating beam and synthetic data
generated by the Harmonic Oscillator ODE,
u''+cu'+ku=0, u(t_0)=u_0 and u'(t_0)=0,
are contained within. For details read README.txt once you have downloaded and unzipped the file. This is a zip file.