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Lecture
Image Processing I: Linear Operators and Fourier Transform
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Quantum Mechanics: Mathematical Framework
Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.
Bounded Operators: Theory and Applications
Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.
Image Processing I: Ordered Dithering and Fourier Transform
Explores ordered dithering and Fourier transform in image processing.
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Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.
Edge Detection: Basics and Techniques
Introduces the basics of edge detection, including measuring contrast, gradient images, Fourier interpretation, Gaussian functions, Canny edge detector, and industrial applications.
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Covers image smoothing, noise reduction, and segmentation techniques using filters and transforms.
Fourier Transform: Concepts and Applications
Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.
Numerical Methods: Boundary Value Problems
Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.
Fourier Transform: Properties and Applications
Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.
Fourier Transform: Properties and Convolution
Covers the properties and convolution of the Fourier transform.
