Schedule: Thursdays: 3:30-6:00 pm, GOV 104 Tompkins 201 (note location change)

Instructor: Poorvi Vora, 714 Philips Hall. Office Hours: 2:30-4:00pm, Wednesdays

Text: Avinash C. Kak and Malcolm Slaney, Principles of Computerized Tomographic Imaging, Society of Industrial and Applied Mathematics, 2001 (available free online)

We will be using Piazza for this class. Resources --- such as class slides --- will be posted on Piazza. The instructor will answer questions through Piazza (you may send messages privately if you choose).

Course Content: Classical reconstruction algorithms such as filtered back-projection, Algebraic Reconstructive Technique (ART), Simultaneous Iterative Reconstruction Technique (SIRT). Classical algorithms for the incorporation of prior information in reconstruction, such as Projections Onto Convex Sets (POCS). Papers on modern research problems based on student interest.

Prerequisites: Undergraduate probability and statistics, calculus, linear algebra, programming (matlab is fine)

Grading: HWs and paper presentation. HWs will be assigned every week. They will be simple, and will reinforce ideas taught in class.

Planned Schedule This is very tentative and will change considerably based on student response

17 January, Lecture 1: Projections and Line Integrals. Shepp and Logan Phantom. Section 3.1 from text (lhs of equation 6 should be P'(θ, t)). Refer to section 2.1.1 and 2.2.1 for the one and two-dimensional Dirac delta functions (ignore equations 100, 107, and the discussion on point sources and point spread functions). (we will do Dirac delta functions in Lecture 2 later lecture on Filtered Back Projection) HW 1: Use matlab to generate phantom and projection data for various types of slices, varying spatial and angular resolution.

24 January, Lecture 2: One and two-dimensional Dirac delta functions (sections 2.1.1 and 2.2.1; ignore equations 100, 107, and the discussion on point sources and point spread functions). Projections as sums (section 7.1) and Algebraic Reconstructive Technique (ART, section 7.2). See excellent description of matlab tools by Per Christian Hansen and Maria Saxild-Hansen HW 2: ART examples.

31 January, Lecture 3: Simultaneous Iterative Reconstructive Technique (SIRT, section 7.3).

7 February, Lecture 4: Convergence properties of ART and SIRT. HW 3: SIRT examples.

14 February, Lecture 5: Undergraduate presentation of mini-projects. Fourier Series and Transforms as choice of basis.

21 February, Lecture 6: Fourier Slice Theorem. Section 3.2.

28 February Lecture 7: Complete Fourier Slice Theorem. Filtered Back Projection. Section 3.3.

7 March - 25 April Lectures 8-14: Student Presentations