Image Processing I: Convolutional Neural Networks

This lecture covers the basics of convolutional neural networks (CNNs) for image processing, starting with an introduction to artificial neurons and neural network architectures. The instructor explains the composition properties of CNNs, including multi-channel convolution operators and pointwise nonlinearities. Practical aspects such as pooling, denoising, and segmentation are also discussed. The lecture delves into the formal model of neurons, operator-based formalism, and the convolutional layer in detail. Additionally, the concept of vector-valued convolutional layers and the composition properties of nonlinear operators are explored. The lecture concludes with a discussion on the properties of composition in deep neural networks, emphasizing the preservation of linearity. Various examples and applications are presented throughout the lecture.