This course gives an introducion on mathematical models and techniques for various image processing tasks. A wide array of topics will be covered, including image restoration (denoising, deblurring), image decomposition, image segmentation, image registration, feature detection, multi-scale image analysis, morphology and so on. Students will become familiar with essential mathematical techniques for imaging tasks, such as image processing in the spatial domain (using gradient, Laplacian, convolution) and frequency domain (using Fourier / wavelet transform). Variational models and PDE-based techniques will also be discussed. Students are expected to have basic knowledge in calculus, linear algebra and MATLAB language. Some background in numerical analysis, Fourier analysis and partial differential equations will be helpful, although the necessary concepts will be discussed as they are used.