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Sept 2, 2009
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Course overview.
Introduction to
mathematical image science.
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Sept 4, 2009
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Math
background: The complex plane, odd/even functions, The Dirac delta
function.
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Sept 7,
2009 |
Labor Day
holiday
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Sept 9, 2009
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Introduction
to
linear systems.
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Sept 11, 2009
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Fourier's
theorem: Fourier series and
the continuous Fourier transform.
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Sept 14, 2009
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Properties
of the Fourier transform.
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Sept 16, 2009
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Gaussian,
sinc, rect, sinusoid, and comb
functions Essential Fourier transform pairs.
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Sept 18, 2009
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The
complex transfer function.
[attached
figure]
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Sept 21, 2009
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The
convolution principle.
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Sept 23, 2009
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The
sampling theorem.
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Sept 25, 2009
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Sampling
and restoration.
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Sept 28, 2009
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Apodizing
and aliasing.
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Sept 30, 2009
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The
Discrete Fourier
Transform (DFT).
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Oct 2, 2009
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The
Discrete Fourier
Transform (DFT) (cont.) [attached
material]
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Oct 5, 2009
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The
edge response
function; edge enhancement. [attached
figures]
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Oct 7, 2009
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Approximate
restoration from sampling
(pixels) [attached
figures] |
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Oct 9, 2009
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Clean up loose ends
and
review. |
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Oct 12, 2009
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First test.Approximate
restoration from sampling
(pixels) [attached
figures] |
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Oct 14, 2009
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Distributions and their
moments:
Expectation, mean and
variance.
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Oct 16, 2009
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The binomial,
Poisson, and
Gaussian distributions. Other distributions.
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Oct 19, 2009
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Fourier
relationships – the
characteristic function. The central limit theorem.
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Oct 21, 2009
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Introduction to
elementary decision
theory. Signal to noise ratio. The Rose model.
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Oct 23, 2009
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Joint and
conditional probabilities;
Bayes' theorem.
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Oct 26, 2009
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Receiver
Operating
Characteristics (ROC).
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Oct 28, 2009
|
Receiver
Operating
Characteristics (ROC). (cont.)
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Oct 30, 2009
|
Principles of
noise averaging: the
covariance concept. Stationary noise. The autocovariance function.
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Nov 2, 2009
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Simulated
1D
normally distributed
stationary noise; demonstration of autocovariance and power
spectrum. [noise
graphs 1] [ng2]
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Nov 4, 2009
|
Simulated
1D
normally distributed
stationary noise (cont.) Effects of
smoothing
on the autocovariance function.
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Nov 6, 2009 |
Apparent
effects
of noise spatial
frequency composition; the power spectrum.
[noise
images] |
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Nov 9, 2009
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The propagation
of error. The
covariance matrix.
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Nov 11,
2009 |
Maximum
likelihood. Linear
regression. The correlation coefficient.
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Nov 13, 2009
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Clean up
loose ends and review
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Nov 16, 2009
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Bivariate linear
regression. The eigenstructure of the covariance matrix. |
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Nov 18, 2009
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Optimization.
The
Levenberg - Marquardt approach. |
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Nov 20, 2009
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Finish optimization section. |
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Nov 23, 2009
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The
2D Fourier transform and the Central
Slice Theorem |
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Nov 25,
2009 |
Imaging
from
projections: The sinogram. [projection
picture] |
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Nov 27, 2009
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Thanksgiving
break. |
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Nov 30, 2009
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Analytic
reconstruction
methods. |
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Dec 2, 2009
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Consequences
of
discretization: sampling considerations in imaging from
projections. ISMRM
poster
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Dec 4, 2009
|
Pixel
transformations: Part I: the 2D affine
transformation. Part
II: The
anti-aliasing affine transformations.
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Dec 7, 2009
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Mutual
information.
Pre-2004
image registration
lecture. |
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Dec 9, 2009
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Expectation
-
maximization. |
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Dec 11, 2009
|
OSEM
Image
reconstruction. |
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Dec 14, 2009
|
The analysis of
variance. |
Medical
Physics/BME
573
- Image
Science (Fall 2009)