Infopaket

Mathematical Methods of Diagnostics Data Processing

ОК 10

Обов’язкова дисципліна для ОП

Second

2024/2025

2 Semester

3

Students should learn the main methods used when working with medical diagnostic data and the results of applied and fundamental research in the field of biophysics. Students must know the first-order optimization methods (Gradient Descent, its derivatives) and second-order optimization methods (Levenberg-Marquardt); the Principal Component Analysis (PCA) method, K-means clustering, and Gaussian Mixture Models (GMM); the specifics of using Fourier and Wavelet transforms for signal processing. The Supervised Learning paradigm and the principles of model hyperparameter tuning, loss functions, and metrics for evaluating models used for various tasks. The student should be able to: Select and use the optimization methods; reduce data dimensionality using the PCA-method;apply various types of spatial filters for image processing tasks; use different methods for tuning neural network hyperparameters and to evaluate model effectiveness using various metrics.

Full-time form

The student should know: the basic concepts of calculus, such as the derivative, gradient, extremum, and integral;the fundamentals of working with discrete signals; the specifics of signal decomposition into series, the Fourier integral; the Discrete and Fast Fourier Transform (DFT and FFT);the fundamentals of programming.

The course focuses on the essential methodologies for processing experimentally acquired data across different dimensions. Key topics include parameter estimation using various first- and second-order optimization algorithms as well as derivative-free approaches. A concise overview is provided for dimensionality reduction techniques (Principal Component Analysis - PCA, Singular Value Decomposition - SVD) and clustering algorithms (k-Means, Gaussian Mixture Models - GMM). Furthermore, the curriculum introduces fundamental processing methods based on spatial or frequency signal filtering, applications of Fourier and Wavelet transforms, and Machine Learning techniques.

1. Steven L Brunton, J Nathan Kutz Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control - Cambridge University Press, -Cambridge,England- 2022. - 248 c. 2. Ian Goodfellow, Yoshua Bengio,Aaron Courville Deep Learning - MIT Press -Cambridge, USA - 2014-720p. 3. Mykel J.Kochenderfer,Tim A.Wheeler Algorithms for Optimization - MIT Press - Cambridge, USA - 2019-520p. 4. Rafael C. Gonzalez, Richard E. Woods' - Digital Image Processing, Fourth Edition- Pearson - London,England - 2010 - P. 1022 5. Rasmus R. Paulsen - Introduction to Medical Image Analysis - Springer Nature -London,England - 2020- P. 186

Lectures 28 hours

The 2 midterm examinations, each of which is graded with a maximum of 30 points. The minimum score for each test must be 18 points. Assessment of individual work. A pass/fail exam, with a maximum possible grade of 40 points. The condition for admission to the exam is obtaining 36 points during the semester. The condition for achieving a positive grade for the discipline is obtaining a minimum of 60 points overall, and the score for the exam cannot be less than 24 points.

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