------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. A. Demonstrate "total variation" regularization and compare results to Tikhonov. Starting point: http://www2.imm.dtu.dk/~pch/mxTV/ ------------------------------------------------------------- B. Implement Tikhonov and truncated SVD regularization for a color image where the RGB channels do not interact but have the same blurring function. Should the same regularization parameter be used for all channels? Implement Tikhonov and truncated SVD regularization for a color image where the RGB channels interact, so that the blur function couples them. ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. C. Suppose we take 5 (blurred) pictures of the same scene. Demonstrate how can we use this extra data to get a better deblurred result. ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. D. Demonstrate how much the choice of boundary conditions (true, black, periodic, or reflexive) can affect the deblurred image. Starting point: HNO Section 3.5 ------------------------------------------------------------- E. Demonstrate Tikhonov regularization, but include upper and lower bounds on the pixel values -- for example, 0 and 255. Compare with our usual methods. Starting point: http://www.mathworks.com/help/toolbox/optim/ug/lsqlin.html ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. F. Demonstrate how to analyze the texture of an image. Starting point: http://www.mathworks.com/help/toolbox/images/f11-27972.html ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. G. Demonstrate 3 algorithms for denoising. Starting point: http://www.mathworks.com/help/toolbox/wavelet/ug/f5-1006048.html ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. H. Demonstrate the transformations involved in going from a "raw" camera image to the one stored in jpeg format. Starting point: http://en.wikipedia.org/wiki/Raw_image_format ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. I. Demonstrate how to reconstruct a brain image from raw MRI data and its "blurring" function. Starting point: http://dukemil.bme.duke.edu/MRI/Simulation/filterresulthp.html http://www.biij.org/2008/1/e15/e15.pdf ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. J. Demonstrate how to reconstruct a brain image from raw CAT scan data and its "blurring" function. Starting point: http://bookstore.siam.org/CL33 ------------------------------------------------------------- K. Demonstrate how our methods can be used on 1-dimensional data rather than on images. Starting point: Consider problems such as phillips, shaw, and spikes in http://www2.imm.dtu.dk/~pch/Regutools/ ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. L. Demonstrate how an iterative method like LSQR can be used for regularization, and explain why it works. Starting point: http://www.mathworks.com/help/techdoc/ref/lsqr.html Section 7.7 of HNO ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. M. Demonstrate the use of the Canny edge detector and compare it with another method. Starting point: http://www.mathworks.com/help/toolbox/images/ref/edge.html ------------------------------------------------------------- N. Demonstrate the use of the k-means algorithm for clustering pixels by gray level and compare it with another method. Starting point: http://www.mathworks.com/help/toolbox/stats/kmeans.html ------------------------------------------------------------- O. Implement an automatic method to use statistical diagnostics to choose a regularization parameter. Starting point: software I can provide from http://www.cs.umd.edu/users/oleary/reprints/j87.pdf ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. P. Demonstrate the steps in JPEG compression and how it works. Starting point: http://en.wikipedia.org/wiki/JPEG ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. Q. Demonstrate the use of high-pass and low-pass filters on images, and compare with TSVD regularization. Starting point: http://www.mathworks.com/help/toolbox/images/ref/fspecial.html http://www.mathworks.com/help/toolbox/images/ref/imfilter.html ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. R. Experiment with different Tikhonov regularization terms -- measuring the norm of the image, or its gradient, or its 2nd derivatives, etc. -- and demonstrate which features they reconstruct best. Starting point: HNO Section 7.3 ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. S. Demonstrate and explain the use of the FFT for TSVD when the blurring operator is constant and boundary conditions are periodic. Starting point: BCCB discussion in Chapter 4 of HNO ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. T. Demonstrate how to determine the blurring function directly from the image and then deblur. Starting point: http://people.csail.mit.edu/billf/papers/deblur_fergus.pdf ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. U. Determine the blurring function for your own camera (under some particular set of conditions) and try to deblur an image. ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. V. Demonstrate a technique to remove an unwanted feature from an image (ex-spouse, grafitti on a wall) and fill in a reasonable approximation to the background. Starting point: http://en.wikipedia.org/wiki/Inpainting ------------------------------------------------------------- PROJECT ALREADY ASSIGNED TO A STUDENT. W. Demonstrate the use of the Lucy-Richardson deblurring algorithm and compare it with our methods. Starting point: http://www.mathworks.com/help/toolbox/images/bqqhlbw.html -------------------------------------------------------------