Mathematical Models and Methods for Image Processing (MMMIP)

Politecnico di Milano — A.Y. 2025/2026
Prof. Giacomo Boracchi

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Course Overview

No neural networks — only expert-driven algorithms with clear mathematical modeling that admit closed-form solutions and sound optimization schemes.

Topics

#	Topic	Notebook	Description
1	Representation w.r.t. Orthonormal Basis	lez_01_orthonormal_basis.ipynb	Builds and analyzes 1D DCT bases, orthogonality, projections and sparse coefficients.
2	DCT Basis for Images & Image Compression (JPEG)	lez_02_DCT_images.ipynb	Introduces 2D DCT dictionaries for image patches and JPEG-style compression/reconstruction.
3	Image Denoising: Sliding DCT	lez_03_DCT_denoising.ipynb	Implements image denoising with smoothing, patchwise DCT sparsity, hard thresholding and Wiener filtering.
4	Away From Orthonormal Bases & Limitations of Sparsity	lez_04_limitations_of_sparsity.ipynb	Compares sparsity in orthonormal and redundant dictionaries, with denoising and Tikhonov regularization examples.
5	PCA Denoising	lez_05_Global_PCA_denoising.ipynb	Uses PCA/data-driven bases to denoise images from noisy patch observations.
6	Matching Pursuit	lez_06_matching_pursuit.ipynb	Implements greedy sparse approximation with Matching Pursuit over redundant dictionaries.
7	Matching Pursuit Variants	lez_07_matching_pursuit_variants.ipynb	Extends the sparse coding workflow with alternative pursuit strategies and coefficient updates.
8	Sparse Inpainting	lez_08_Inpainting.ipynb	Restores missing image pixels by combining patch dictionaries, masks and OMP-based sparse reconstruction.
9	OMP Denoising	lez_09_OMP_Denoising.ipynb	Applies Orthogonal Matching Pursuit to patch-based image denoising with redundant dictionaries.
10	Dictionary Learning (K-SVD)	lez_10_KSVD.ipynb	Learns dictionaries from image patches with K-SVD and uses them for OMP denoising and texture modeling.
11	Gradient Descent	lez_11_gradient_descent.ipynb	Studies least-squares optimization, objective visualization and iterative gradient descent updates.
12	Non-Local Means & Self-Similarity	lez_12_NLMeans.ipynb	Explores image self-similarity and implements Non-Local Means denoising.
13	ISTA	lez_13_ISTA.ipynb	Solves L1-regularized sparse coding/LASSO problems with the Iterative Shrinkage-Thresholding Algorithm.
14	FISTA	lez_14_FISTA.ipynb	Accelerates ISTA with FISTA momentum for faster L1-regularized optimization.
15	IRLS, MOD & L1 Denoising	lez_15_IRLS_MOD_l1Denoising.ipynb	Compares IRLS and FISTA for L1 sparse coding and applies the workflow to dictionary-based denoising.
16	Sparse Anomaly Detection	lez_16_Anomaly_Detection.ipynb	Detects anomalies by learning a normal dictionary, estimating sparse reconstruction errors and thresholding detections.
17	Local Polynomial Approximation (LPA)	lez_17_LPA.ipynb	Builds standard and weighted LPA kernels and applies centered, left and right filters to synthetic signals.
18	Adaptive LPA-ICI	lez_18_LPA_ICI.ipynb	Selects the local scale adaptively with the ICI rule and combines left- and right-sided estimates through aggregation.
19	2D and Anisotropic LPA-ICI	lez_19_LPA_ICI_2D.ipynb	Extends LPA-ICI to image denoising with multiscale isotropic and directional kernels, selected scales and PSNR evaluation.
20	Robust Fitting	lez_20_Robust_Fitting.ipynb	Compares OLS and DLT line fitting under outliers and implements RANSAC, MSAC and LMedS robust estimators.
21	Multi-Model Fitting	lez_21_Multi_Model_Fitting.ipynb	Uses Sequential RANSAC to detect multiple lines and circles in the Stair, Star and circle datasets.

Repository Structure

MMMIP/
├── code/          # Jupyter notebooks — lab assignments & solutions
└── README.md

License

Educational use only. Course materials belong to Prof. Giacomo Boracchi.

Valutazione

10/10