An inverse problem course

This Learning Resources page is all about inverse problems. It focuses on the problem of image deconvolution and resolution enhancement. It offers various documents (in PDF format): slideshow for lectures, exercise topics and practical matlab-work.

Lectures

• [PDF] Introduction and examples
• [PDF] Linear solutions: least-square and inverse filtering, quadratic penalty and Wiener-Hunt solution
• [PDF] Convex penalty and edge preservation: Huber and half-quadratic approach
• [PDF] Positivity and support constraints, Alternative Direction Methods of Multilpliers
• [PDF] Quadratic minimization, system solvers, matrix inversion: a short and partial view
• [PDF] An example in astronomy: bi-model, smoothness and parsimony, positivity and support, ADMM
• [PDF] An example in radar imaging: high resolution and sparsity, ADMM
• [PDF] Concluding remarks and perspectives

Exercises

• [PDF] Circulant matrices, quadratic functions, Legendre transform, linear constraints, sparsity, denoising,…

MatlabWork

• [PDF] Linear solutions and filtering: quadratic penalty and Wiener-Hunt
• [PDF] Bayesian standpoint and stochastic sampling for hyperparameter estimation.
• [PDF] Convex penalty and edge preservation: Huber and half-quadratic approach.
• [PDF] Positivity constraints and ADMM.