COMPGV08  Inverse Problems in Imaging
This database contains 201718 versions of the syllabuses. For current versions please see here.
Code  COMPGV08 (Also taught as COMPM078) 

Year  MSc 
Prerequisites  This course requires good mathematical and programming skills. In particular students should be familiar with :

Term  2 
Taught By  Simon Arridge (100%) 
Aims  To introduce the concepts of optimisation, and appropriate mathematical and numerical tools applications in image processing and image reconstruction. 
Learning Outcomes  To understand the principles of optimisation and to acquire skills in mathematical methods and programming techniques. 
Content
Introduction
 Example problems
 Data Fitting Concepts
 Existence
 Uniqueness
 Stability
 Bayesian interpretation
Mathematical Tools
 Linear Algebra
 Solving Systems of Linear Equations
 Over and Under Determined Problems
 EigenAnalysis and SVD.
 Variational Methods
 Calculus of Variation
 Multivariate Derivatives
 Frechet and Gateaux Derivatives
 Regulariation
 Tikhonov and Generalised Tikhonov
 NonQuadratic Regularisation
 NonConvex Regularisation
 Methods for selection of regularisation parameters
Numerical Tools
 Descent Methods
 Steepest Descent
 Conjugate Gradients
 Line Search
 Gauss Newton and Full Newton
 TrustRegion and Globalisation
 QuasiNewton
 Inexact Newton
Newton Methods
Optimisation Methods
 LeastSquares Problems
 Linear Least Squares
 Nonlinear Least Squares
 NonQuadratic Problems
 Poisson Likelihood
 KullbackLeibler Divergence
 Lagrangian penalties and constrained optimisation
 Proximal methods
Concepts of sparsity
 L1 and total variation
 wavelet compression
 dictionary methods.
Bayesian Approach
 Maximum Likelihood and Maximum A Posteriori estimates
 ExpectationMinimisation
 Posterior Sampling
 ConfidenceLimits
 Monte Carlo Markov Chain
Applications
 Image Denoising
 Image Deblurring
 Inpainting
 Linear Image Reconstruction
 Tomographic Reconstruction
 Reconstruction from Incomplete Data
 NonLinear Parameter Estimation
 General Concepts
 Direct and Adjoint Differentiation
Other Approaches
 Learning Based Methods
Method of Instruction
Lecture presentations with associated class coursework and laboratory sessions
Assessment
The course has the following assessment components:
 Written Examination (2.5 hours, 75%)
 Coursework (2 pieces, 25%)
To pass this course, students must:
 Obtain an overall pass mark of 50% for all sections combined.
Resources
Reading list available via the UCL Library catalogue.