Web Page for Math 514
Fall Semester 2007: Numerical Linear Algebra and Inverse Problems
Spring Semester 2008: Computational and Statistical Inverse Problems.
Syllabi
Riff-raff for course discussion, Fall 2007
DEBLURRING: First, here are some examples of true and blurred image and a reconstruction of the satellite obtained by computing A^{-1}b here , where the matrix A is defined using the discrete PSF given here. And here are a two schemata on ill-posedness: 1, 2. Finally, we've got an example with a true, blurred and reconstructed image here.
ADAPTIVE OPTICS: For an explanation of this, see these slides from a talk given in Zurich PDF, movie.
Web site for the course text "Deblurring Images: Matrices, Spectra, and Filtering", P.C. Hansen, J. Nagy, and D. P. O'Leary, SIAM 2006.
Riff-raff for course discussion, Spring 2008
Web site for the course text "Computational Methods for Inverse Problems", Curt Vogel, SIAM 2002.
Homework
POLICY: (FOR THE MOST PART) NO LATE WILL BE HOMEWORK ACCEPTED.
Fall 2007:
Assignment #1 (9/5), PDF.
Assignment #2 (9/19), PDF.
Assignment #3 (9/26), PDF.
Assignment #4 (10/08), PDF, challenge2.mat. See Lab 3 m-file below.
Assignment #5 (10/17), PDF.
Assignment #6 (10/26), PDF, HW6.m, kronDecomp.m.
Assignment #7 (11/9), PDF, Lab6.m.
Spring 2008:
Assignment #1, PDF.
Assignment #2, PDF.
Assignment #3, PDF.
Assignment #4, PDF.
Assignment #5, PDF.
Codes for Labs and Lectures and Lab Assignments
Fall 2007:
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Lab 1: Code for solving Poisson equation with unit forcing and homogeneous, Dirichlet boundary conditions on the unit square: poisson.m.
Code for adaptive optics simulation and estimation: AOneD.m, AOTwoD.m.
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Lab 2 (10/3): Code BlurringLabKronecker.m, BlurringLabGaussian.m, and psfGauss.m.
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Lab 3 (10/5): (i) Plot the singular values of Ar generated in BlurringLabKronecker.m; (ii) Plot the singular vectors corresponding to the first, fifth, twenty-fifth, and fiftieth singular values; (iii) do the same for Ac; (iv) Implement the truncated singular value decomposition to obtain a regularized solution, what seems to be the optimal truncation value? Here's part (iv) is done BlurringLabKroneckerTSVD.m
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Lab 4 (10/19): We can now fully understand BlurringLabGaussian.m. Implement the TSVD filter in this case. I'm also getting you started on Assignment 5 with this code Challenge8temp.m. For that you'll need iocolor512.tif.
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Lab 5 (10/22): In this lab, we discuss creating realistic data. For this we'll need Lab5.m, iogray.tif and iograyBorder.tif. You'll also need the following files: dcts.m, idcts.m, dcts2.m, idcts2.m, dctshift.m, padPSF.m
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Lab 6 (10/24): Using Lab5.m and Lab6.m with 1% noise, compute the naive solutions of the deblurring problem in the periodic and reflexive boundary condition cases. Next, use the TSVD to compute regularization solutions for both periodic and reflexive boundary conditions. Do the truncation levels differ? Do the boundary conditions have an effect? Finally do the same for the defocuse blurr psfDefocus.m.
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Lab 7 (10/31): (i) Implement the Tikhonov filter for the data in challenge2.mat. You may use my MATLAB code for HW #4 HW4.m. Can you read the small lettering now? (ii) Also, implement the Tikhonov filter in BlurringLabGaussian.m and Lab5.m.
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Lab 8 (11/09): Using gcv_tsvd.m, which implements generalized cross validation for TSVD regularization, modify both HW4.m and BlurringLabKroneckerTSVD.m so that they implement GCV for regularization parameter choice. Using gcv_tik.m, modify BlurringLabGaussian.m and HW4.m so that it implements Tikhonov regularization with GCV for regularization parameter choice.
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Lab 9 (11/19): Download Jim Nagy's RestoreTools MATLAB package.
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Lab 10 (11/26): Download the following codes for the final project FinalProjectCodes.zip.
Spring 2008:
- Lab 1 (2/1/2008): Down load the following MATLAB codes as well as the accompanying PDF: Lab1HW1.pdf, Gen_data.m, Driver_cg.m, cg.m, A_mult.m, satellite.mat.
- Lab 2 (2/6/2008): Download the following MATLAB codes: AOSolver.m, AO.mat.
- Lab 3 (2/8/2008): Download the following PDF: Lab3HW2.pdf.
- Lab 4 (2/27/2008): Download the following PDF Lab4HW3.pdf and ZIP file RestoreTools.zip.
- Lab 5 (3/10/2008): Download the "Nonnegatively Constrained Convex Programming Codes Algorithm" MATLAB codes at MATLAB codes.
- Lab 6 (4/2/2008): Download these Kalman Filter MATLAB codes.
- Lab 7 (4/21/2008), here are some files to download: OneDToeplitz_CG.m, OneDToeplitz_GenData.m, optimal_circ_toep.m, circulant.m, my_toeplitz.m. First generate data, then run CG to obtain a regularized solution of Kf=d. What is the optimal regularization parameter? After doing this, modify the CG driver so that optimal circulant preconditioned CG is implemented instead. Create a plot comparing the performance of the two methods.
- Lab 8 (4/23/2008), here are some files to download: GenData.m, extract.m, bttb.m, Demo_fourier.m, fourier.m, GenData.m, convolve_2d.m, Deblur_fourier.m.