Chapter I: Introduction
- The is the problem you're doing
- Why is it important?
- What has been done?
- What are your original contributions?
- What are the impacts of your work?

Chapter II: The 1D AM-FM Signal Model
2.1 What is the AM-FM Model?

2.2 Instantaneous Frequency
	2.2.1 The importance of IF
	2.2.2 Debates on IF

2.3 Computation of the 1D AM-FM Signal Model
	2.3.1 Analytic Signal
	2.3.1 Teager-Kaiser Energy Operator
	2.3.3 Quasi-local AM-FM Estimation
2.4 Comparison of 1D AM-FM Techniques

2.5 Summary



Chapter III: The 2D AM-FM Image Model
3.1 The AM-FM Image Model: A Review
	3.1.1 What is the AM-FM Image Model?
	3.1.2 Computation of the AM-FM Image Model
	3.1.3 Multidimensional IF

3.3 Complex Image Extension
	3.3.1 Partial Hilbert Transform
	3.3.2 Total Hilbert Transform
	3.3.3 Single Orthant approach
	3.3.4 Adjusted Hilbert Transform
	3.3.5 Hypercomplex
	2.4.6 Larkin's spiral phase and Felberg's Monogenic

3.3 nD IF: Other Approaches
	3.3.1 The Teager-Kaiser approach
	3.3.2 Gilomari and Vakman quasi-local approach

3.4 Comparison between nD IF extension approaches

3.5 Summary


Chapter III: The PR AM-FM Image Transform
3.1 The AM-FM image model
3.2 The Analysis AM-FM model
3.3 The perfect reconstruction AM 
3.4 The perfect reconstruction FM 
	3.2.1 Spline-based
	3.2.2 Least square
3.5 The perfect reconstruction AM-FM transform

Chapter IV: AM-FM image processing
4.1 AM-based
4.2 FM-based
4.3 AM-FM based
4.4 Summary

Chapter V: Extensions
5.1 Monogenic phase ambiguity --> fixed up
5.2 Pinwheel transform
5.3 Noisy estimation

Chapter VI: Conclusion and Future Work

Chapter VII: Appendices
