Unit MATHEMATICAL METHODS FOR ARTIFICIAL INTELLIGENCE

APPLIED IMAGE AND SIGNAL PROCESSING

Code	A002085
CFU	6
Teacher	Gianluca Vinti
Teachers	Gianluca Vinti
Hours	52 ore - Gianluca Vinti
Learning activities	Affine/integrativa
Area	Attività formative affini o integrative
Sector	MAT/05
Type of study-unit	Obbligatorio (Required)
Language of instruction	English
Contents	Introduction to the course • Summary of the Fourier transform and its properties. • Exact sampling and approximate sampling • Generalized sampling operators and sampling- Kantorovich: their properties and main results. • Notions on images and on the applications of the theorem of sampling to images • MATLAB and its applications to image processing • GIMP, IMAGEJ, and their applications to image processing • Image Processing Algorithms: registration, segmentation, thresholding, morphological operators, smoothing and sharpening operators, etc. • Image acquisition instrumentation: CT, RNM, Thermography. • Medical diagnostics: -General introduction to medical diagnostics - Vascular, diagnostic and interventional surgery • Possible visits: - Visit to the Diagnostic Imaging Department: radiography (RX), computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, cardioCT. -Visit to the section of vascular surgery: endovascular treatments -Visit the ophthalmology section • Visit to the Center for Research on Atomic Pollution and the Environment (Hot-Box, thermography, thermal bridges and pollution). • Non-invasive diagnostics in the engineering field: image processing for seismic vulnerability • Laboratories of Applied Mathematics on topics of the course
Reference texts	Notes and slides of the teacher. It will be recommended some books.
Educational objectives	Learning outcomes: The course provides knowledge of the major concepts of image processing with particular reference to the medical ones. The main knowledge (descriptor Dublin 1) will be acquired: • knowledge of the reconstruction of signals and images by sampling; • Knowledge of the main concepts and analysis techniques and image processing; • knowledge of the main problems of medical diagnostics and application of algorithms for the improvement of image; The main skills acquired (ability to apply the knowledge gained descriptor Dublin 2, and to take with independent judgment the appropriate approach, the Dublin descriptor 3) will be: • analytical skills and image processing whose purpose is to medical diagnosis; • ability to develop a line of reasoning that leads the student to identify the methods of solving the problem in question; • ability to identify the right approach to the solution of the problem with an eye toward the medical diagnostics.
Prerequisites	Knowledge of reconstruction of signals and images by sampling; Knowledge of the main concepts and analysis techniques and image processing; Knowledge of the main problems of medical diagnostics and of the application of algorithms for the improvement of image.
Teaching methods	The course is structured as follows: 1) Lectures on all the topics of the course; 2) Classroom workshop: 2/3 workshops on problems where topics from the course are used 3) Guided tours of 4 hours each at the departments of the Santa Maria della Misericordia Hospital in Perugia (radiology and / or vascular and / or ophthalmology surgery) and / or at Engineering.
Other information	Attendance is strongly recommended for all lessons.
Learning verification modality	Oral exam. The verification of the educational objectives of teaching (examination) include an oral exam. The oral exam will be held on the dates set out in the examinations of the CdS calendar. The oral examination, consists of a discussion of the duration not exceeding 40 minutes each aimed at verifying: i) the level of knowledge of the theoretical and laboratory course content (Dublin descriptor 1), ii) the level of expertise in exposing the logical and mathematical reasoning skills (descriptor Dublin 2), iii) the independence of judgment (Dublin descriptor 3) to propose the most appropriate approach to argue what is required. The oral examination also aims to verify the student's ability to present with properties of language questions proposed by the Commission, to support a dialectical relationship during discussion and dimostrate logical-deductive ability and synthetic exposition (descriptor Dublin 4). The final mark will be made by the Commission in thirty.
Extended program	Introduction to the course • Summary of the Fourier transform and its properties. • Exact sampling and approximate sampling • Generalized sampling operators and sampling- Kantorovich: their properties and main results. • Notions on images and on the applications of the theorem of sampling to images • MATLAB and its applications to image processing • GIMP, IMAGEJ, and their applications to image processing • Image Processing Algorithms: registration, segmentation, thresholding, morphological operators, smoothing and sharpening operators, etc. • Image acquisition instrumentation: CT, RNM, Thermography. • Medical diagnostics: -General introduction to medical diagnostics - Vascular, diagnostic and interventional surgery • Possible visits: - Visit to the Diagnostic Imaging Department: radiography (RX), computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, cardioCT. -Visit to the section of vascular surgery: endovascular treatments -Visit the ophthalmology section • Visit to the Center for Research on Atomic Pollution and the Environment (Hot-Box, thermography, thermal bridges and pollution). • Non-invasive diagnostics in the engineering field: image processing for seismic vulnerability • Laboratories of Applied Mathematics on topics of the course
Obiettivi Agenda 2030 per lo sviluppo sostenibile

NUMERICAL METHODS FOR INFORMATION TECHNOLOGIES

Code	A002084
CFU	6
Teacher	Gianluca Vinti
Teachers	Bruno Iannazzo (Codocenza)
Hours	47 ore (Codocenza) - Bruno Iannazzo
Learning activities	Affine/integrativa
Area	Attività formative affini o integrative
Sector	MAT/08
Type of study-unit	Obbligatorio (Required)
Language of instruction	English (or Italian upon request).
Contents	Numerical aspects of approximation, linear algebra and optimization with application to Data Science and Information Technologies.
Reference texts	Slides of the course will be provided by the teacher. The textbook is: J. Stoer, R. Bulirsh. Introduction to numerical analysis. Springer. 2013. For optional arguments the reference will be communicated during the course.
Educational objectives	Get into the mathematical aspects of some important applications to Data Science and Information Technologies. Ability to work out all the aspects of the mathematical modelling, from abstract mathematics to its model interpretation and the computer simulation.
Prerequisites	Linear algebra. Differential calculus of function or real variables.
Teaching methods	Lectures and MATLAB laboratory.
Learning verification modality	Oral exam. The oral exam can be substituted with a mid term seminar and a final project. The objective of the oral exam is to examine how the student manage the topics of the course. The objective of the mid term is to examine the ability to present a topic related to the course but studied autonomously.
Extended program	Least squares approximation and singular value decomposition (principal component analysis). QR factorization and nonnegative matrix factorization. Trigonometric interpolation and Fast Fourier Transform. Nonlinear optimization and manifold optimization. Applications: data fitting; classification problems; machine learning.