Rochester Institute of TechnologyRochester, New YorkCOLLEGE of ScienceDepartment of Imaging ScienceNEW (or REVISED) COURSE: 1051-4531.0 Title: IMAGING SYSTEMS III: Noise & Random Processes Date: ___________Credit Hours: __4__Prerequisite(s): SIMG-452 (Imaging Systems II)SIMG-xxx (Probability & Statistics for Imaging)Corequisite(s): __________________________________________Course proposed by: __________________________________________ 2.0 Course information: Contact hours Maximum students/sectionClassroom 3 30Lab 3 12Studio Other (specify _______)Quarter(s) offered (check)_____ Fall _____ Winter __X__ Spring _____ SummerStudents required to take this course: (by program and year, as appropriate)___SIMG majors________________________________________Students who might elect to take the course: _____________________ 3.0 Goals of the course (including rationale for the course, when appropriate): To provide students with practical skills in the mathematical analysis and modeling ofrandom noise in imaging systems. Students will be able to measure, characterize, anddiagnose the causes of noise in complex systems of imaging processes. 4.0 Course description (as it will appear in the RIT Catalog, including pre- and co-requisites, quarters offered)1051-5xx Imaging Systems III: Noise & Random ProcessesThis course applies the mathematical and computational skills acquired in previous courses to the analysis and modeling of noise and random processes in a sequence of imagingprocesses. Experimental techniques for measuring noise will be studied and practiced. Noise characteristics of imaging systems will be modeled based on mathematical probability and moment theory. Jacobian operators and Fourier theory will be used to model correlated noise and to propagate noise properties through complex sequences of imaging processes. Practical metrics of noise and signal/noise ratios will be examined for their utility as figures of merit for imaging systems. (1051-5xx) Class 3, Lab 1,Credit 4 (S)5.0 Possible resources (texts, references, computer packages, etc.)5.1 Lecture notes provided by the instructor 5.2 Reading assignments from:5.2.2 Fundamentals of Electronic Imaging Systems, 2nd Ed. by W.F. Schreiber, (Springer-Verlag, 1991).5.2.3 An Introduction to Microdensitometry, by Richard E. Swing, SPIE, 1998.6.0 Topics (outline):6.1 Early Experimental Observations6.1.1 Visual Merging Distance6.1.2 RMS granularity measurements 6.1.3 Selwyn's Law6.2 The Probability Density Function6.2.1 The image histogram and RMS granularity6.2.2 Expectation calculations6.2.2 Moment theory and useful theorems6.3 Bernoulli Trials and Modeling a Detector6.3.1 The Bernoulli PDF6.3.2 Poisson PDF6.3.1 Quantum noise limit of noise6.3.2 Signal/noise in a quantum limited detector6.3.3 Transmittance and reflectance modeled as Bernoulli Trials6.3.4 Small noise propagation approximation: D vs R 6.4 Bernoulli Trials in a Detector Array: Image Noise6.4.1 The basic checkerboard model and assumptions6.4.2 Imaging Elements and the Fundamental limit of granularity6.4.3 Signal/noise in a quantum limited detector array6.4.4 Comparison with experimental systems6.4.4.1 Image Capture: CCD camera6.4.4.2 Image Output: Electrophotographic toner image6.4.5 The checkerboard model and the Tone Curve6.5 Propagation of Noise through Multiple Imaging Processes6.5.1 Noise Propagation Theorem & useful approximations 6.5.2 Characteristics of multiple noise sources6.5.3 Propagation of the PDF6.5 Correlated Statistics of Noise6.5.1 Experimental observations: Selwyn Law Failure6.5.2 Modified Checkerboard model of Selwyn Law Failure6.5.3 The joint-PDF6.5.4 Covariance, auto-covariance, and auto-correlation6.5.5 Fourier theory of correlated noise: Wiener Spectrum6.5.6 Signal/Noise metrics and information capacity6.6 Experimental Manifestations of the Wiener Spectrum6.6.1 Wiener Spectrum vs measurement aperture6.6.2 Aperture effect on the measured PDF6.6.3 Correlated checkerboard model6.6.3.1 Derivation of Deriving Selwyn's Law and Failure6.6.3.2 Derivation of Wiener Spectrum vs Aperture6.7 Propagation of Correlated Noise through Multiple Imaging Processes6.7.1 Propagation of the Wiener Spectrum: The TTF and MTF6.7.2 Propagation of the joint-PDF: Jacobian, TTF and MTF6.8 Visual Noise6.8.1 Noise metrics vs visual perception (Engeldrum IQ circle)6.8.2 Visual CTF and visual granularity6.8.3 Halftones, moiré, and frequency shifting6.9 Laboratory Exercises 6.7.1 RMS granularity and Selwyn's Law6.7.2 Measurement of Wiener Spectrum6.7.2.1 Aperture effect 6.7.2.2 Instrument MTF6.7.3 Quantum noise characteristics of a CCD camera6.7.4 Noise Through a System: Camera and Printer6.7.3.1 Propagating input noise6.7.3.2 Parsing out the camera noise6.7.3.3 Parsing out the printer noise6.7.5 Noise Through a System: Camera, Digital Operator, Printer6.7.5.1 Modeling the system6.7.5.2 Tone reproduction vs noise propagation7.0 Intended learning outcomes and associated assessment methods of those outcomesThe successful student will be able to:7.1 Describe and mathematically model the factors governing noise and signal/noise ratio in a sequence of imaging processes. (homework, labs, exams)7.2 Perform mathematical analysis of noise properties of imaging systems using moment theory and Fourier analysis. (homework, labs, exams)7.3 Make experimental measurements of RMS granularity and Wiener spectra, and interpret the data with regard to the measurement aperture, instrument MTF, and measurement noise. (labs)8.0 Program or general education goals supported by this courseThis course provides students with quantitative skills in the experimental and mathematical analysis of noise and random processes in systems of imaging processes. 9.0 Other relevant information (such as special classroom, studio, or lab needs,special scheduling, media requirements, etc.)Teaching laboratories on the 3rd floor of building 76 will be used. 10.0 Supplemental