Exam 1 Review

“Review” for Exam 1, BMEN 420 Medical Imaging
The material covered is found in selected portions of Chapters 1-5 of Medical Imaging Signals and Systems by
Prince and Links. Specifically, however, consider the following:
a. Chapter 1 [Introduction] was covered with
i. introductory powerpoint, lecture 1, (know concepts, not dates)
ii. part of hmwk 1, part of quiz 1
iii. general coverage:
1. various imaging modality definitions, signal sources, characteristics, the
electromagnetic spectrum and medical imaging
b. Chapter 2 [Signals and Systems] was covered with
i. Lectures, FT handouts, Matlab examples
ii. Part of Hmwk 1, part of quiz 1, part of Hmwk 2
iii. General coverage:
1. Specific signals of use (impulse function(s), sampling functions, rect, sinc, complex
exponentials, sinusoidal)
2. How to make use of those signals
a. be able to understand and use the impulse/delta function as you had to in the
homework questions and quiz #1
b. Understand spatial frequencies – units, sketching, what it means, where the
spatial frequency plots in x and y are present in the F.T. equation and what
the meaning is of multiplying them times the object f(x,y) and integrating over
all space – i.e. understand how Fourier/frequency/(u,v) space is filled.
3. Linear Shift Invariant systems and the impulse response/PSF/h(x,y)
a. Understand, somewhat mathematically and completely conceptually, linearity
and shift invariance (several class examples as well as hmwk #1 questions and
quiz #1 questions)
b. Input-output equations given the psf …. Convolution
i. What does convolution do physically and mathematically (this does
not mean you would have to convolve mathematically with anything
other than a delta function, but understand what convolution does
and how it is used). Know the integral and understand that it “flips
and shifts”. Understand the integral to the point that you could write
it if you needed to.
4. The Fourier Transform
a. Know the equation (memorize it) and what it means with regard to spatial
frequency content. See comments in 2b of this review. Understand the
integral.
b. Know the commonly used FTs from the chart and supplemental FT handouts
[you would be expected to know that Gaussians transform to Gaussians,
deltas to unity, sins and cosines to deltas (why?), sincs to rects (know the
relationship between widths as you change domains – i.e. scaling – more
localization in one domain means less in the other)]
c. Understand the properties of the FT and be able to use the pertinent ones
that you have seen multiple times (scaling, translation, rotation, separability,
convolution, product)
5. The Transfer Function, H(u,v), that is the FT of the psf, h(x,y)
6. Sampling & Nyquist: **hmwk 2 covered this well and this is an important concept**
Once our system “band limits” our signal by multiplying the input by H(u,v) which has
a cutoff frequency, then we know how fast we need to sample so as not to suffer from
aliasing.
c. Chapter 3 [Image Quality] was covered with
i. Lectures, supplemental ppt graphics for contrast/resolution, Artifact ppt
ii. Part of Hmwk #2
iii. General coverage:
1. Contrast: *the MTF* as the normalized, one-dimensional function, obtained from the
transfer function, H(u,v) – a frequency domain concept. **why do we normalize? Why
are we able to use only one dimension?** Use of a pure sinusoid (pure frequency) to
understand contrast. See supplemental ppt graphics. Understand relationship to
hmwk #2 question #7c.
2. Resolution: *the FWHM* from the psf – a spatial domain concept. See supplemental
ppt graphics. If given an MTF (frequency domain), know how to obtain resolution from
a cutoff frequency (frequency domain) or from the FWHM (spatial domain). Examples
worked in class.
3. Signal to Noise Ratio –know the concept
4. Artifacts: what are they? covered conceptually with ppt. Be familiar with types of
artifacts encountered in various modalities.
5. Distortion: understand in context of projection imaging (i.e. depth dependent
magnification in projection x-ray)
6. Accuracy: understand the model for diagnostic accuracy and its
advantages/disadvantages
d. Chapter 4 [Physics of Radiography] (this includes physics of x-ray and CT) was covered with
i. Physics of radiography ppt – large parts of this presentation were omitted. Understand
concepts/definitions of ionizing radiation, how it can interact with atoms, what the
“advantages” and “disadvantages” are of the interactions – with regard to biological concerns
and imaging ability, the linear attenuation coefficient and what causes attenuation
e. Chapter 5 [Projection Radiography] was covered with
i. Introductory notes (2 pgs, typewritten, electronic) on conventional/projection radiography
instrumentation, Image Formation lecture notes
ii. Our first specific modality – understand attenuation model, *4 geometric effects* - 3 of which
need to be mathematically represented in the imaging equation, effects of the system
(sources of blurring and effects on the imaging equation, including problem 5.12 worked in
class, the fundamental tradeoff in x-ray imaging when trying to increase the SNR, the general
effect of Compton scattering).
In general, study the lectures, the powerpoints, and the homeworks. For unclear concepts from the lecture, consult
the book. You will not be expected to do nasty or meaningless math. You will not be expected to memorize obscure FT
relationships or properties. You will not be expected to “prove” anything. Understand the material to the best of your
ability, particularly material that fits into the larger concepts of the course.