Lecture Slides

Lectures

Course logistics

• Lecture 0: How This Course Works (logistics, grading, labs)

Chapter 1 · Introduction

• Lecture 1 (Aug. 24): What is Computational Imaging?

Chapter 2 · Probability, Estimation, and Random Processes

• Lecture 2 (Aug. 26): Random Variables and Expectation
• Lecture 3 (Aug. 28): Commonly Used Distributions
• Lecture 4 (Aug. 31): Frequentist and Bayesian Estimators
• Lecture 5 (Sept. 2): Discrete-Time Random Processes

Chapter 3 · Causal Gaussian Models

• Lecture 6 (Sept. 4): Causal Prediction in Gaussian Models
• Lecture 7 (Sept. 9): 1-D Gaussian Autoregressive Models
• Lecture 8 (Sept. 11): 2-D Gaussian AR Models

Chapter 4 · Noncausal Gaussian Models

• Lecture 9 (Sept. 14): Noncausal Prediction in Gaussian Models
• Lecture 10 (Sept. 16): 1-D and 2-D Gaussian Markov Random Fields
• Lecture 11 (Sept. 18): GMRF vs. AR Models

Chapter 5 · MAP Estimation with Gaussian Priors

• Lecture 12 (Sept. 21): MAP Image Restoration; Computing the MAP Estimate
• Lecture 13 (Sept. 23): Gradient Descent Optimization
• Lecture 14 (Sept. 25): ICD, Preconditioning, and Conjugate Gradient

Chapter 6 · Non-Gaussian MRF Models

• Lecture 15 (Sept. 28): Non-Gaussian MRFs, Potential and Influence Functions
• Lecture 16 (Sept. 30): Convex Potentials and the Scale Parameter

Chapter 7 · MAP Estimation with Non-Gaussian Priors

• Lecture 17 (Oct. 2): MAP Estimation with Non-Gaussian Priors

Chapter 8 · Surrogate Functions and Majorization

• Lecture 18 (Oct. 5): Surrogate Functions and the MM Algorithm
• Lecture 19 (Oct. 7): Surrogate Properties, and Building the Quadratic Surrogate
• Lecture 20 (Oct. 9): Reweighting, and the One-Step Optimal Line Search

Chapter 9 · Constrained Optimization and Proximal Methods

• Lecture 21 (Oct. 14): Constrained Optimization; Lagrangian Duality
• Lecture 22 (Oct. 16): The Augmented Lagrangian
• Lecture 23 (Oct. 19): Proximal Maps and Shrinkage
• Lecture 24 (Oct. 21): Variable Splitting
• Lecture 25 (Oct. 23): The ADMM Algorithm: Applications and Convergence

Chapter 10 · Plug-and-Play and Advanced Priors

• Lecture 26 (Oct. 26): Plug-and-Play: Motivation; Plug-In Denoisers
• Lecture 27 (Oct. 28): Consensus Equilibrium for Two Models
• Lecture 28 (Oct. 30): Multiagent Consensus Equilibrium

Chapter 12 · The EM Algorithm

• Lecture 29 (Nov. 2): The EM Algorithm: Motivation, and Gaussian Mixture Distributions
• Lecture 30 (Nov. 4): EM Theory; EM for Gaussian Mixtures
• Lecture 32 (Nov. 9): EM Clustering; Convergence and Majorization
• Lecture 33 (Nov. 11): Simplified EM Update Derivations

Chapter 13 · Markov Chains and Hidden Markov Models

• Lecture 34 (Nov. 13): Markov Chains and Their Estimation
• Lecture 35 (Nov. 16): Hidden Markov Models (Highlights)
• Lecture 36 (Nov. 18): Stationary Distributions of Markov Chains
• Lecture 37 (Nov. 20): Properties of Markov Chains

Chapter 14 · General MRF Models

• Lecture 38 (Nov. 23): MRFs and Gibbs Distributions; the Ising Model

Chapter 15 · Stochastic Simulation

• Lecture 39 (Nov. 30): Simulation; the Metropolis Sampler
• Lecture 40 (Dec. 2): The Hastings–Metropolis Sampler; Stochastic Sampling of MRFs
• Lecture 41 (Dec. 4): The Gibbs Sampler

Course review

• Lecture 42 (Dec. 7): Course Review

To be determined

• Lecture 43 (Dec. 9): To be determined
• Lecture 44 (Dec. 11): To be determined

Slides are posted here as the semester progresses.

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