Class Schedule 2010
Principles of Neuroimaging A, Fall, 2010 - Class Schedule and Syllabus Back to main course page
Week 1: Orientation to Neuroimaging, Neurons, Brains
Monday 9/27/10 - Orientation & Neurons. Speaker: Mark Cohen
In this first class we will review the basics of neurophysiology with an eye towards what signals of brain function might be visible to the neuroimager. We will discuss information coding, energetics, size and time scales.
'Required Readings'
Suggested Further Reading
- This paper, by Malhi, is a nice orientation in methods of neuroimaging. *Making sense of neuroimaging in psychiatry
Wednesday 9/29/10 - The Organization of the Human Brain. Speaker: Susan Bookheimer
We will discuss the general organization of the human brain, and the regional specialization of cortical areas. The emphasis will be on understanding principles of organization:
- Phylogenetic Layering
- Functional Specialization
- Principles Divisions of the Brain
- Brain Systems
Required Readings
Suggested Further Reading
- Problem Set 1 Neuroanatomy. Due in class 10/6.
We will be studying linear systems next week. This coming week until Monday would be a good time to review your calculus fundamentals:
- Derivatives of Polynomials
- Integrals of polynomials
- Basic trig + derivatives and integrals of sine and cosine functions
When we start on the linear systems section, we will be using these fundamentals to develop the LaPlace and Fourier transforms, which involve the use of imaginary numbers. The math content for that section is largely contained in this link: Mathematical Tools.
Please let me know by email or other means if this material looks too difficult.
You will need to have matlab installed and running to do the next problem set.
Week 2: Linear Systems
Why the emphasis on Linear Systems? Because they are actually easy (as compared to non-linear systems, which are not.) As we go through this course, we will see many ways in which linear systems theory is applied to:
- Modeling of Neural Systems
- Extraction of Signal from Noise
- Design of Circuits
- Image Enhancement
- Understanding of Image artifacts, and others.
Linear systems analysis is one of the great technologies of the 20th and 21st century. It is now the basis for virtually all electronics design, and its extension into the discrete (digital) domain is the basis for most of modern signal processing.
In our specific case, we will use these few basic principles of linear systems to understand both the instruments we use and the neuroimaging signals we collect. When you have mastered this material, you should be in a much better position to model the systems that you study in order to develop an approach to studying them.
Monday 10/4/10 - Transforms and the Convolution Theorem. Speaker: Mark Cohen
Required Readings
- van Drongelen: Chapter 1
- Mathematical Tools
Suggested Further Reading
- Problem Set 2A - Introduction to matlab
Please see MATLAB linearity demo
If you are the type who sees beauty in mathematics, the Euler identity may be one of the most beautiful pieces of math in the world.
Wednesday 10/6/10 - Fourier Transform Properties. Speaker: Mark Cohen
- Example transform derivations
- The Convolution theorem
- Oddness (and Even-ness)
- The Fourier Shift Theorem
Please see MATLAB demo of Fourier transforms and convolution
Optional Readings:
- van Drongelen: Chapters 5 through 9
- Note: This reading may be heavy going. I will not be going into nearly this much detail in class, but your time on this will be very well spent. We will be revisiting this material later in the course in week 5.
Suggested, Optional Readings from DSPguide.com:
- Note: These chapters are lite on math and try to focus on a conceptual understanding
- Problem Set 2B modeling in matlab
Problem Set 2A and Problem Set 2B
I suggest very strongly that you brush up on linear algebra during this week in anticipation of Dr. Sugar's lectures in statistics. In particular, I would like you to have an understanding of :
- Matrices as solutions to linear equations - determinants and inverses
- Matrix multiplication
For these, I can recommend the Hefferon text noted above.
Week 3: Noise and Basic Statistics
Monday 10/11/10 - Noise. Speaker: Mark Cohen
It is what you don't want.
- Additive noise
- White Noise
- Boltzmann noise
- Colored Noise
- Gaussian Noise
- Coherent noise
- Sampling Errors
- Aliasing
- Quantization noise
- Spectral filtering
Noise comes in all shapes and colors. It is present in every measurement we make, from an EEG voltage to an estimate of the effects of dopamine on forebrain signal. Our best weapons are an understanding of the statistical properties of noise, the sources of noise and the ways to control it. Noise in the discrete digital domain is special, as it is both created by digitization and amplified by sampling.
Readings:
- van Drongelen: Chapters 2 through 4
- Slides used in Class:
Noise Slides
- Problem set 3 - properties of noise
Wednesday 10/13/10 - Statistical Fundamentals. Speaker: Catherine Sugar, Director of the NPI Statistics Core
We will consider the general problems of statistical inference, with a concentration on developing an intuitive understanding of statistical concepts.
Review of:
- Descriptive Statistics: mean, mode, variance, standard deviation
- Statistical Inference. The Binomial and Normal Distribution
- Basic Tests: t-test, linear correlation
- Modeling and non-linear relations
- Bayes rule
Suggested reading
- The latter teaches stats at what I feel to be the right level - developing intuitions about the kinds of questions that can be answered using stats and about the statistical tests and measures
- Problem Set 5 - Statistics in matlab
Week4: Statistics for Imaging
Monday 10/18/10 - Statistics for Imaging I. Speaker: Catherine Sugar, Director of the NPI Statistics Core
- Outline
Required Readings
- The General Linear Model
- Linear Algebra applied to Statistical Solutions
- Analysis of Variance
Suggested Further Reading
Wednesday 10/20/10 - Statistics for Imaging II. Speaker: [#URL]
- Fixed and Random Effects
- Repeated measures
- Bonferroni and Other Corrections
- Non-Parametric Methods
- Autocorrelation
- Unknown Distributions
Required Readings
Suggested Further Reading
Week 5: Optics
Monday 10/25/10 - Optics I. Speaker: [mailto: Zachary Taylor]
- Outline
Required Readings
Suggested Further Reading
Wednesday 10/27/10 - Optics II. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Week 6: #TOPIC
Monday 11/1/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Wednesday 11/13/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Week 7: #TOPIC
Monday 11/8/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Wednesday 11/10/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Week 8: #TOPIC
Monday 11/15/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Wednesday 11/17/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Week 9: #TOPIC
Monday 11/22/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Wednesday 11/24/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Week 10: #TOPIC
Monday 12/1/10 - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Wednesday #DATE - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Week #NUM: #TOPIC
Monday #DATE - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Wednesday #DATE - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Week #NUM: #TOPIC
Monday #DATE - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Wednesday #DATE - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Week #NUM: #TOPIC
Monday #DATE - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading
Wednesday #DATE - #LECTURE. Speaker: [#URL]
- Outline
Required Readings
Suggested Further Reading