Mathematical processing of signals and images

Baklanova Olga Evgenyevna

The instructor profile

Description: The main tasks of signal theory. Orthogonal transformations in the processing of signals and images. The main features of the discrete transformation of Fourier. Matrix representation of correlations and switches. Svertki's theorem. Algorithms for the formation of orthogonal rectangular functions. Representation of signals in the form of Walsh functions. The main provisions of wavelet analysis. Getting images. Preliminary processing of images. Basic image conversion. Rotation, scale change and displacement of images. Segmentation of the image by means of the separation of the border area. Operator Roberts. Operator Previtta. Operator Sobella. Transformation of Karunena-Loeva. Data compression model.

Amount of credits: 3

Пререквизиты:

  • Mathematical Analysis 2

Course Workload:

Types of classes hours
Lectures 15
Practical works 15
Laboratory works
SAWTG (Student Autonomous Work under Teacher Guidance) 30
SAW (Student autonomous work) 30
Form of final control Exam
Final assessment method

Component: Component by selection

Cycle: Base disciplines

Goal
  • The purpose of this course is to study the basics of mathematical signal and image processing.
  • study of modern methods of mathematical description of digital signal and image processing systems
Objective
  • study of mathematical methods for modeling and processing signals and images, which can be used to solve a wide range of problems in various fields of science and technology.
  • obtaining practical skills in design, as well as research of signal and image processing systems in the MatLab environment
Learning outcome: knowledge and understanding
  • дискретті сигналдар теориясын білу
Learning outcome: applying knowledge and understanding
  • be able to build mathematical models of signals and images
  • synthesize digital filters
  • develop and use digital signal processing algorithms
Learning outcome: formation of judgments
  • formation of students' minimum necessary knowledge, skills and abilities in digital signal and image processing
Learning outcome: communicative abilities
  • independent work with special literature and teamwork
  • be capable of social interaction
  • have the ability for interpersonal communication
  • be able to work in a team
Learning outcome: learning skills or learning abilities
  • self-formulation and solution of new engineering problems in the field of signal and image processing
Teaching methods

The main educational technologies are oral presentation of theoretical material, showing presentation material in lectures, performing tasks in practical classes.

Topics of lectures
  • Signals and their features
  • Orthogonal transformations in signal and image processing tasks
  • Matrix representation of correlations and switches
  • Algorithms for the formation of orthogonal rectangular functions
  • Representation of signals in the form of Walsh functions
  • Multidimensional transformations for image processing
  • Basic principles of wavelet analysis
  • Algorithms for computing the Haar transform
  • Image acquisition
  • Basic image transformations
  • Spatial and frequency domain techniques applied to image pre-processing
  • Segmentation of the image by highlighting the boundaries of areas
  • Basic properties of the two-dimensional Fourier transform
  • Basics of filtering in the frequency domain
  • Compression of data
Key reading
  • Гонсалес Р., Вудс Р. Цифровая обработка изображений Издание 3-е, исправленное и дополненное Москва: Техносфера, 2012. – 1104 с.
  • Применение цифровой обработки сигналов//- Под.ред. А.Оппенгейма.- М. –Мир. -1980.-550 с.
  • Рабинер Л.,Гоулд Б. Теория и применения цифровой обработки сигналов.//-М. – Мир. -1978. - 545 с.
  • Сергиенко, А. Б. Цифровая обработка сигналов : учеб. пособие. 2-е изд. / А. Б. Сергиенко. – СПб. : Питер, 2006.
  • Основы цифровой обработки сигналов: курс лекций / А. И. Солонина, Д. А. Улахович, С. М. Арбузов, Е. Б. Соловьева. СПб. : БХВ-Петербург, 2005.
  • Ричард, Л. Цифровая обработка сигналов : пер с англ. 2-е изд. / Л. Ричард. М. : Бином-Пресс, 2007.
Further reading
  • Тропченко А Ю., Тропченко А.А. Цифровая обработка сигналов. Методы предварительной обработки. Учебное пособие по дисциплине "Теоретическая информатика". – СПб: СПбГУ ИТМО, 2009. – 100 с.
  • Ханов, В. Х. Цифровая обработка сигналов : учеб. пособие для студентов специальности 090301 «Информатика и вычислительная техника» очной формы обучения / В. Х. Ханов, Д. А. Никитин ; Сиб. гос. аэрокосмич.ун-т. – Красноярск, 2014. – 156 с.
  • Скляр, Б. Цифровая связь: Теоретические основы и практическое применение : пер с англ. 2-е изд. / Б. Скляр. М. : Вильямс, 2004.
  • Айфичер, Э. С. Цифровая обработка сигналов: практический подход: пер. с англ. 2-е изд. / Э. С. Айфичер, Б. У. Джервис – М. : Вильямс, 2004.
  • Alexiadis D. S., Sergiadis G. D. [2007]. Estimation of Multiple Accelerated Motions Using Chirp-Fourier Transforms and Clustering. IEEE Trans. Image Proc., vol. 16, no. 1, pp. 142–152.