Unit MEDICAL IMAGING ALGORITHMS

Course
Mathematics
Study-unit Code
55A00055
Curriculum
Matematica per le applicazioni industriali e biomediche
Teacher
Laura Angeloni
Teachers
  • Laura Angeloni
Hours
  • 42 ore - Laura Angeloni
CFU
6
Course Regulation
Coorte 2022
Offered
2022/23
Learning activities
Caratterizzante
Area
Formazione teorica avanzata
Academic discipline
MAT/05
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italian
Contents
Brief introduction to classical Signal Theory: continuous and discrete signals, their main properties.
Reconstruction of signals by sampling and applications. Digitale Images and some algorithms of Digital Image Processing. Filtering in the spatial and in the frequency domain. Images compression and redundancy.
Reference texts
Lecture notes and slides by the teacher. Some books will also be advised.
Educational objectives
The aim of the course is to reach competence about the main concepts of signal and image processing.

The main knowledge (Dublin Descriptor 1) acquired will be:
- knowledge of the basic notions of classical signal theory
- knowledge of signal reconstruction by means of sampling
- knowledge of basic notions on digital images
- knowledge of some of the main image processing algorithms
- knowledge of the main filtering algorithms

The main skills acquired (ability to apply the acquired knowledge, Dublin Descriptor 2, and to adopt with autonomous judgement the suitable approach, Dublin Descriptor 3) will be:
• ability to describe and analyze the main image processing algorithms;
• ability to develop reasoning with autonomous judgement and to identify the right approach to solve problems concerning image processing.
Prerequisites
Basic notions of Mathematical Analysis.
Teaching methods
Frontal lessons.
Other information
Some laboratory activity could be held with the aim to deepen some applicative aspect of the course.
Learning verification modality
The verification of teaching educational goals is through an oral exam. The interview will be held on the dates set out in the examinations calendar of the related Corso di Studi.
The oral exam consists of a discussion of about 40 minutes with the aim to verify i) the level of knowledge and understanding achieved by the student on the program's issues (Dublin 1 descriptor), ii) the level of competence in expressing one's own capacity for logical-mathematical argumentation, as well as in applying the studied concepts to concrete problems (Dublin 2 descriptor), iii) the autonomy of judgment (Dublin 3 descriptor) in proposing the most appropriate approach to develop what required. The oral tests also have the objective of verifying the student's expository and communication skills, with particular attention to the property of language and the ability of self-organization of the exposition on the theoretical contents of the course (Dublin 4 descriptor).

For information on support services for special needs students, please visit the page https://www.unipg.it/en/international-students/general-information/facilities-for-special-needs-students .

In any case, the teacher is available to personally evaluate, in specific cases, any compensatory measures and / or personalized paths in the case of students with special needs and also in case of working students or students that are not able to attend lessons.
Extended program
- Introduction to Signal Theory: physical, mathematical, deterministic, random, multi-dimensional signals.
· Theory of continuous signals: definition of continuous signals, examples, symmetry, translation, area and mean value, energy and power, duration and extension of a signal. Periodic signals, periodic repetition and area, mean value, energy, power, duration and extension of a periodic signal. Examples of main signals: constant, sinusoidal, exponential, step, rectangular signals, ideal impulses (Dirac delta), sync-type impulse. Convolution, properties, durability and convolution calculation.
· Series and Fourier transform: definitions and main properties of the series and Fourier transform.
· Band of a signal and examples of transforms of some important signals. Signals Filtering: a study in the time domain and frequency domain.
· Theory of discrete signals and their main properties. Fourier transform for discrete signals.
· Multi-dimensional Fourier transform. DFT and FFT transform: definitions and computational complexity.
· Reconstruction of signals by sampling: history, Shannon sampling theorem and its consequences and applications.
- Digital images, gray-scale and color images. Multidimensional sampling: sampling theorem for images. Aliasing Phenomena. Spatial, spectral, radiometric, temporal resolution. Zoom and shrink of a digital image.
- Digital image operations. Introduction to Image Processing in the spatial domain. Punctual, local, global transformations.
- Histogram of gray tones: definition and main features. Examples of histogram transformations.
- The noise. Image enhancement through arithmetic operations.
- Spatial filtering: smoothing and sharpening filters. Filtering in the frequency domain.
- Image Compression: redundancy, lossless and lossy compression, video compression.
Condividi su