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Sept 3, 2008
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Course overview.
Introduction to
mathematical image science.
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Sept 5, 2008
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Math
background: The complex plane, odd/even functions, The Dirac delta
function.
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Sept 8, 2008
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Introduction
to
linear systems.
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Sept 10, 2008
|
Fourier's
theorem: Fourier series and
the continuous Fourier transform.
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Sept 12, 2008
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Properties
of the Fourier transform.
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Sept 15, 2008
|
Gaussian,
sinc, rect, sinusoid, and comb
functions Essential Fourier transform pairs.
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Sept 17, 2008
|
The
complex transfer function. [attached
figure]
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Sept 19, 2008
|
The
convolution principle.
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Sept 22, 2008
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The
edge response
function; edge enhancement. [attached figures]
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Sept 24, 2008
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The
sampling theorem. |
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Sept 26, 2008
|
Sampling
and restoration.
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Sept 29, 2008
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Apodizing
and aliasing.
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Oct 1, 2008
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The
Discrete Fourier
Transform (DFT)
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Oct 3, 2008
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The
Discrete Fourier
Transform (DFT) (cont.) [attached
material]
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Oct 6, 2008
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Approximate
restoration from sampling
(pixels) [attached
figures]
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Oct 8, 2008
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Clean up loose ends and review.
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Oct 10, 2008
|
First
Test.
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Oct 13, 2008
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Distributions and their
moments:
Expectation, mean and
variance.
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Oct 15 2008
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The binomial,
Poisson, and
Gaussian distributions. Other distributions.
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Oct 17, 2008
|
Fourier
relationships – the
characteristic function. The central limit theorem.
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Oct 20, 2008
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Introduction to
elementary decision
theory. Signal to noise ratio. The Rose model.
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Oct 22, 2008
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Joint and
conditional probabilities;
Bayes' theorem.
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Oct 24, 2008
|
Receiver
Operating
Characteristics (ROC).
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Oct 27, 2008
|
Receiver
Operating
Characteristics (ROC). (cont.)
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Oct 29, 2008
|
Principles of
noise averaging: the
covariance concept. Stationary noise. The autocovariance function.
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Oct 31, 2008
|
Simulated
1D
normally distributed
stationary noise; demonstration of autocovariance and power
spectrum. [noise
graphs 1] [ng2]
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Nov 3, 2008
|
Simulated
1D
normally distributed
stationary noise (cont.) Effects of
smoothing
on the autocovariance function.
|
| Nov 5, 2008 |
Apparent
effects
of noise spatial
frequency composition; the power spectrum.
[noise
images] |
|
Nov 7, 2008
|
The propagation
of error. The
covariance matrix.
|
|
|
| Nov 10,
2008 |
Maximum
likelihood. Linear
regression. The correlation coefficient.
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Nov 12 2008
|
Clean up
loose ends and review
|
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Nov 14, 2008
|
Second
test. |
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Nov 17 2008
|
The
2D Fourier transform and the Central
Slice Theorem. |
|
Nov 19, 2008
|
Imaging
from
projections: The sinogram. [projection
picture] |
|
Nov 21, 2008
|
Analytic
reconstruction
methods.
|
|
|
| Nov 24,
2008 |
Consequences
of
discretization: sampling considerations in imaging from
projections. ISMRM
poster |
|
Nov 26, 2008
|
Pixel
transformations: Part I: the 2D affine
transformation. Part
II: The
anti-aliasing affine transformations. |
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Nov 28, 2008
|
Thanksgiving
break.
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Dec 1, 2008
|
Mutual
information.
Pre-2004
image registration
lecture.
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Dec 3 2008
|
Optimization.
The
Levenberg - Marquardt approach. |
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Dec 5, 2008
|
Expectation
-
maximization. OSEM
Image
reconstruction. |
|
|
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Dec 8, 2008
|
Expectation
-
maximization. OSEM
Image
reconstruction. |
|
Dec 10, 2008
|
The analysis of
variance.
|
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Dec 12, 2008
|
Bivariate linear
regression. The eigenstructure of the covariance matrix.
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Medical Physics/BME
573
- Image
Science (Fall 2008)