Time schedule: We have nearly 6 weeks until the final project presentations on Dec 20. Let us proceed along the following time schedule (you can always accomplish the tasks earlier, these are just deadlines):

Nov 14	Pick at least 3 projects that interest you and email me their titles. You can rank them.
Nov 21	Research the topic and form some thoughts on how you would accomplish the task. Use google and  the SBU electronic library to mine the world for information. If you cannot locate a paper, let me know. Schedule an appointment with me to discuss your solution. Likely you will gain much more information in that meeting. But do come informed.
Dec 5	Email me a first progress report, or create a webpage on which you report your progress (in that case email me the link). List the papers, books, and webpages you found useful. Outline your solution approach. Report you first results. Update the webpage as you go. I will monitor it. Feel free to stay in touch, for questions and to get further insight. But be aware that I cannot do the work for you.
Dec 18	Make available the second progress report. At this point you should be very close to the final conclusion.
Dec 20	Have a powerpoint presentation on your project ready, and perhaps even a demo. We will allocate a seminar-type session where all students will present their results. Undergraduates will also be invited. So dress (your ppt file) to impress.

Theme: Since we discussed mostly CT up to now I have focused the projects on this modality, but you could do your final project on other modalities as well. Just let me know. Also, you are not constrained to work on the topics mentioned below. You can propose your own and send me a proposal. Finally, you may work in a team of two, but then the project extent and outcome must be scaled up appropriately.

Deliverables: A report and a presentaton. Make sure you test it all with a good variety of images and system setting. You are expected to study your algorithms and program in a scientifc manner, using plots with quality metrics and reconstructed images. The report should communicate the insight you have gained in terms of understanding the behavior of the algorithm, its strengths and its weaknesses.

Data: Medical imaging is mostly about reconstruction of an object or phenomenon from data acquired using some type of detector or transducer. I believe that the best approach is to create the data yourself, so you can learn about the process that generated them. Medical imaging is often called an "Inverse Problem" and in fact a journal exists of that name, which is popular in medical imaging. So if you know the physics and process behind the data acquisition, then you are on a good path to propose a solution. Of course, for the matter of this project, you can simplify a lot. For example, you do not have to model beam hardening if your project is not about its compensation. It is recommended to first conduct thorough experiments in 2D. You could use CT slice images you find on the web and utilize matlab's radon and fanbeam transforms to generate the data. In addition you could also use images shown the respective papers which are usually simple phantoms.
The 3D case should be attempted only once you are happy with the 2D performance. I will prefer solutions that go all the way in 2D and offer a good level of insight and sophistication. I rather not see 3D solutions in which most of the time was spent with data generation but which did not get to the heart of the topic at all. However, if you work in a team then you could split the data generation and data processing task.
For 3D we have many 3D datasets here (for volume datasets see here and also here). Check them out -- you will need a 3D projector to generate the data. This link offers a cone beam projector for matlab. We have also mathematical phantom models. In fact, it is always good to start with a very simple 3D object first. This can be as simple as a high-contrast sphere. So the first step would be to create software for simulating the data acquisition first, at the level of complexity that you need to proof your point. Then you can use the simulator as part of your reconstructor, in many cases.

List of topics: Following is a list of topics. As mentioned, you can suggest one of your own, but the complexity should match that of the projects given below. In some cases, projects can be combined, going less deep and wider instead. If you have skills in GPU-accelerated computations, by all means, put them to use. All projects are of similar difficulty. I do strive to distribute the projects evenly among the students, that is, I hope that no project is selected twice, or if so, different solution approaches are pursued. Note, you can find the papers referred to below by simply typing their titles into google. Some require the university online library, so simply do this at a PC within the university domain or log into the university online library site.

1. Exact CT. The M-line approach provides a very general way to do this. This paper describes it in detail: Jed Pack et al (2005). "Cone-beam econstruction using 1D filtering along the projection of M-lines," Inverse Problems 21 1105-1120. Use it to reconstruct volumes from data not only acquired along a circular trajectory, but also along more general arcs. You could try this first with 1D data and 2D reconstruction and compare it with filtered backprojection. [J. Jin, H. Peng]
2. Iterative CT. Iterative algorithms are an alternative to the CT algorithms based on the Radon transform. They have their roots in numerical optimization. We discussed a few methods in class. For this project you would implement and compare them with filtered backprojection reconstruction for these three low-dose CT settings: (i) small numbers of projections, (ii) noisy projections (use matlab's imnoise function with Possion or Gaussian noise); and (iii) reduced angle (less than the typical 180 degs + fan-angle). Study different levels for each, all the way up to the extreme cases. Implement (i) steepest descent, (ii) conjugate gradients, (iii) SART, and (iv) expectation maximization (EM). The formulas and algorithms are in the class notes -- they all involve a projector (use matlab's transforms), a backprojector (you could use the one you wrote for lab3) and some object and projection level manipulations. Make sure you get all the scaling factors right so all the components work well with one another. [L. Hou, M. Keralapura + K. Yendamuri, C. Sun]
3. Regularized iterative CT #1: In these adverse imaging conditions (study all of those listed in 2. just above) it can be useful to enforce certain constraints inbetween reconstruction iterations. One of these is Total Variation Minimization (TVM) which enforces local smoothness (reducing noise and streaks). Matlab has an implementation of it, see here. First just alternate between SART and TVM. Then implement an algorithm that chooses the parameters widely based on the reconstruction result obtained so far See Sidky and Pan, "Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization," Physics in Medicine and Biology, 53: 4777-4807, 2008. [M. Baig, D. Venkatachalam, F. Yang]
4. Regularized iterative CT #2: For the same purpose than 3. study the algorithm proposed in Yu and Wang, "A soft-threshold filtering approach for reconstruction from a limited number of projections,"Physics in Medicine and Biology, 55:3905-3916, 2010. This is an interesting and very promising algorithm! [Y. Zhang. B. Wang, B. Piel]
5. Regularized iterative CT #3: Again, for the same purpose than 3. study the algorithm proposed in Jørgensen et al. "Accelerated gradient methods for total-variation-based CT image reconstruction," Fully 3D 2011. It is a mathematically very elegant solution. It avoids the two-step approach by optimizing local smoothness and data fidelity at the same time. [E. Papenhausen, S. Mahmood]
6. Beam hardening and poly-energetic CT. These are very frequent artifacts and statistically-based methods are well suited to overcome these problems. See the paper: Idris A Elbakri et al . (2003) Segmentation-free statistical image reconstruction for polyenergetic x-ray computed tomography with experimental validation (2003) Phys. Med. Biol. 48 2453-2477. In addition to general artifacts, also specifically simulate metal artifacts which are frequent in dental CT. Compare the outcome with solutions in which you just detect an artifact pixel in the data and then either remove/disregard it or interpolate across it. [S. Nedic]
7. Dynamic CT. Time-varying objects, such as the heart, lungs, or kinematic studies, have to compensate for motion artifacts. A number of techniques have been proposed for this, but it is still an open problem. A few approaches seek to estimate the motion vector of prominent structures and then warp local neighborhoods accordingly, see Ritchie et al. (1996) Correction of computed tomography motion artifacts usingpixel-specific back-projection. IEEE Trans on Medical Imaging, 15(3):333-342. Others backproject (add) new projections to the volume and expire (subtract) olds ones from the volume, see Bonnet et al. (2003) Dynamic X-ray computed tomography. Proceedings of the IEEE, 91(10):1574-1587. The latter creates a reconstruction in which the moving features appear motion-blurred. [A. Goel + S. Dass]
8. Compensation for scattering. Compton scattering becomes a dominating artifact when 2D detectors are used. A popular approach is to reconstruct an object from the data, and then use this reconstruction to model/estimate the scattering with Monte-Calor simulations. The result is then subtracted from the data and a scatter-free object is reconstructed. Some papers are: Kyriakou et al. (2006) Combining deterministic and Monte Carlo calculations for fast estimation of scatter intensities in CT. Phys. Med. Biol. 51, 4567–4586, and also Zaidi et al., (2007) Current status and new horizons in Monte Carlo simulation of X-ray CT scanners. Med Bio Eng Comput. 45(9):809-817. [K. Sun, P. Bhagavatula]
9. Lattices and irrgular grids. It has been shown that optimal lattices, such as BCC, can provide reconstructions at higher accuracy (because of the more isotropic sampling, and this even extends to the detectors themselves). See Xu /Mueller (2007) Applications of optimal sampling lattices for volume acquisition via 3D computed tomography. Volume Graphics Symposium, pp. 57-64. On the other hand, irregular grids can focus high spatial resolution for the reconstruction onto regions where high detail is likely to reside, see Sitek et al. (2006) Tomographic reconstruction using an adaptive tetrahedral mesh defined by a point cloud. IEEE Trans Med Imaging. 25(9):1172-9. Both of these make accurate reconstructions more efficient.   
10. CT of semi-transparent objects and amorphous phenomena. CT can also be used to reconstruct from data obtained with other wavelengths, such as visible, infrared, or laser light. See Trifonov et al. (2006) Tomographic Reconstruction of Transparent Objects. Eurographics Symposium on Rendering for the former and http://www.mpi-inf.mpg.de/~ihrke/publications.html for the latter. [H. Yin. L. Wang, C. Ling, F. Zhang]
11. Low-dose CT by smart projection selection. The number of projections/views, among other factors, determines the dose distributed to the patient. So picking views that maximize the amount of new information for reconstruction is important. The selection of highly informative views has become an important topic for volume visualization and image-based rendering. Most of these approaches use entropy measures. See papers by Vázquez et al. (2003) Automatic View Selection Using Viewpoint Entropy and its Application to Image-Based Rendering, Computer Graphics Forum, pp. 689-700 and  Bordoloi/Shen (2005) Viewpoint Evaluation for Volume Rendering. IEEE Visualization Conference. This project would extend these techniques to X-ray data. While the paper by Wu at al. (2003) Tomographic mammography using a limited number of low-dose cone-beam projection images, Medical Physics. 30(3): 365-380 does not use entropy, it does give good insight on reconstruction issues that arise when a low or semi-irregular number of views is chosen. Iterative reconstruction will be less sensitive to these issues.
12. Special projects as proposed/discussed: [S. Dai, C. Liu, Y. Wang]