Course Syllabus1051-713 Noise and Random ProcessesCourse:SIMG-713 Noise and Random ProcessesFour (4) credit hoursFour (4) lecture hours per weekPrerequisites: 1051-716, 718, 719 or permission of instructorCourse Description:The purpose of this course is to develop an understanding and ability in mod-eling noise and random processes within the context of imaging systems. Theinitial part of the course is an introduction/review of basic probability theoryneeded for the middle part of the course, which introduces random processes.Much of this part of the course will focus on the temporal dimension, as thatdimension is what is emphasized in the textbook. The final part of the coursewill demonstrate the application of the textbook material to the understand-ing of signal and noise in imaging systems. At the completion of the coursethe student should have the ability to model signal and noise transfer within amultistage imaging system.Course Objectives:The student will be able to:• Demonstrate a basic knowledge foundation that enables him/her to de-scribe signals and noise in imaging systems.• Apply a basic knowledge of noise and random processes to the optimizationof S/N in imaging systems.Topic Outline:1. Probability(a) Set definitions and ope rations(b) Introduction to probability(c) Joint and conditional probability(d) Indep e ndent events(e) Combined experiments(f) Bernoulli trials2. Random Variables(a) Random variable concept(b) Distribution function(c) Density function(d) Gaussian RV1(e) Density and distribution examples(f) Conditional distribution and density functions3. Operations on One RV — Expectation and Moments(a) Exp e ctation(b) Moments(c) Functions that give moments(d) Transformations of a RV4. Mutiple RVs(a) Vector RVs(b) Joint distribution and its properties(c) Joint density and its properties(d) Conditional distribution and density(e) Statistical indep e ndence(f) Distribution and density of a sum of RVs(g) Central limit theorem5. Operations on Mutiple RVs(a) Exp e cte d value of a function of a RVs(b) Jointly Gaussian RVs(c) Sampling and some limit theorems6. Random Pro c es se s — Temporal Characteristics(a) RP concept(b) Stationarity and independence(c) Correlation functions(d) Gaussian RPs(e) Poisson RPs7. Random Pro c es se s — Spectral Characteristics(a) Power density spectrum and its properties(b) Relationship b etween power spectrum and autocorrelation function(c) Power spectrums for discrete-time processes and sequences(d) Cyclostationary RPs(e) White noise(f) Photon noise(g) Zero-frequency value of the NPS(h) Noise correlation(i) Zero-Frequency Analysis of Signal and Noise(j) Detective Quantum Efficiency(k) Approaches to defining the performance of detectors(l) DQE in Film Systems(m) DQE Examples2(n) DQE Transfer(o) Photon Amplifier Modeling(p) Cascaded DQE and Quantum Sinks(q) Noise Equivalent Number of Quanta(r) Photon Amplification8. Fourier Analysis of Signal and Noise(a) Autocorrelation Function(b) Noise Power Spectrum(c) Detective Quantum Efficiency(d) Noise Equivalent Quanta(e) Noise Transfer(f) Noise Transfer — Granularity Transfer Example(g) Noise Transfer — Screen-Film System Example(h) Noise Transfer — General Treatment(i) Cascaded DQE(j) Radiographic Screen-Detector System(k) Quantum Accounting Diagram9. Fourier Analysis of Signal and Noise in Digital Systems(a) Detector-element size and aperture MTF(b) Digital MTF: presampling and aliasing(c) Digital Wiener spectrum: presampling and noise aliasing(d) Digital DQE(e) Analysis of a digital detector array(f) System DQEInstructional Techniques:2.1 Textbook information is given below. The textbook will be supplementedwith course notes in weeks 6- 10 which illustrate the applications in imag-ing science.2.2 The lectures will focus on the main points of each chapter, often followingthe textbook or notes very close ly. From the Course Schedule you candetermine what topics will be covered in a particular week. You are ex-pected to read that part of the course notes prior to coming to class sothat you are prepared to discuss the material and ask questions. LectureSlides are posted in the Content section of myCourses.2.3 There are problem sets assigned from the problems at the end of eachchapter in the textbook and these are posted in the Content section ofmyCourses. The problem sets will not be collected. Solutions are postedin the Content section of myCourses. Solutions to problems in Chpts8-10 will be included in the course notes handout later in the quarter.3These problems give you an opportunity to apply probability theory andconcepts. Use these problem sets to test your understanding of coursematerial and to highlight areas needing further study. You can expect tosee similar problems on the exams (see next section).Learning Assessment:3.1 The assessment of your degree of mastery of the course material andachievement of the course objectives is based on your performance on threeexams — one during week 4 (Chpts 1 - 5), one during week 8 (Chpts 6 -8), and a final exam during exam week. The final exam is comprehensive,but weighted toward the final two chapters (50% Chpts 1 - 8; 50% Chpts9- 10). Each exam is worth 100 points, but points missed on the first twoexams carry over to the final exam. For e xample, if you earned 50 pointson exam # 1 and 75 points on exam # 2, you may earn up to 175 pointson the final exam.3.2 All exams are proctored, c lose d-book, problem-type exams consuming amaximum of one hour 50 minutes (two hours for the final exam). Eachexam is designed to test your basic understanding of probability and ran-dom processes, and your ability to apply these tools in solving problems.Problems will be taken from the textbook body (including examples), aswell as the assigned problems at the end of the chapters.3.3 The final grade will be based on the total number of points earned in thethree exams (300 points maximum). The conversion of the final numericalgrade into a course letter grade is based on a curve.Texts:4.1 Required text: Probability, Random Processes, and Random Signal Prin-ciples, Peyton Z. Peebles, 4th Ed. McGraw-Hill, New York, 2001. C oursenotes for Chapters 8-10 will be handed out in week 5.4.2 Reference texts: See individual chapters in textbook and course notes.Contact Information:Instructor: Harvey Rhody, Professor of Imaging ScienceOffice: 17-3173Email: [email protected]: 475-6215Office Hours: By