Instrumentation and Computers in Imaging

Question 1

What is the difference between analogue and digital?

Answer 1

Analogue= continuous (parameters are infinitely variable)
Digital = discrete

Question 2

What is binary?

Answer 2

A useful implementation of discrete because it is a base two number system (0, 1) which can be represented by on/off states of switches (ie. transistors).

Question 3

How does an ADC affect data?

Answer 3

Analogue digital converter = loses data

Sensor: mA -> mV

Question 4

Why doesn’t a transducer produce a perfect signal?

Answer 4

Errors / artefacts
Transfer function
Properties
•	Noise
•	Saturation
•	Linearity
•	Dynamic range
•	Resolution

Question 5

What is the differnce between a perfect and a truthful transducer signal output?

Answer 5

draw graph

• straight line =perfect
• wiggled = truthful

Question 6

What is the process of digital acquisition?

Answer 6

• Digitisation process mangles your data
  o Analogue (continuous) / Digital (discrete)
  o Discrete number system (binary)
  o Acquisition
  • Analogue physical interaction
  • Transducer -> mV / mA
  • ADC converts to binary
  • Calibration – convert numbers to meaningful quantity
  • Binary manipulation in computer
  • Binary interpreted as intensities for image à map
  o Resolution; Bit depth; Linearity; Dynamic range

Question 7

Why does discretisation damage data?

Answer 7

•	Not only is the value of the signal made discrete, but time is discretised too!
•	ADC mangles signal value
•	Latch mangles time
o	Sampling
o	Nyquist sampling rate

Question 8

Why is 44kHz data stream chosen for audio CD?

Answer 8

Human hearing = 20kHz,

Satisfies nyquist sampling rate (2x frequency)

Question 9

How does MRI system work?

Answer 9

o Produces proton density map
o Analogue - RF emissions
o Digitise RF amplitude and phase (ADC)

Question 10

How does Digital X Ray system work?

Answer 10

o Maps X-ray intensity
o Analogue detector is film/CCD
o Digitisation by ADC -> computer

Question 11

What is the series of events for digital imaging?

Answer 11

• continuous quantity
• sensor (transducer - convert to mA/mV)
• ADC (calibration)
• Number (integer in computer)
• Process
• Displace

Question 12

Why does an image not faithfully represent the object?

Answer 12

imagine system does not image a point as a point

• the energy in the object point is smeared over a finite area
• loss of conjugacy with associated degradation of the image
• image becomes a sum of all the point spread functions modulated by the amplitudes of the object at each point

Question 13

What is a point spread function?

Answer 13

smeared representation of the point

Question 14

What is the transfer function?

Answer 14

function that transforms the object to the image

Question 15

When is the transfer function and the point spread function the same?

Answer 15

for an object consisting of a single point

Question 16

What is the amplitude of point spread function modulated by?

Answer 16

amplitude of the object point

Question 17

Where is the point spread function centred?

Answer 17

on the object point

Question 18

On multipoint images, how is the point spread function calculated?

Answer 18

after calculating all the point spread functions distributed across image space, the final image is constructed by added up all the point spread functions at each point

Question 19

What is the convolution integral?

Answer 19

h(u) = integral from negative infinity to positive infinity (f(u-x)g(x).dx

f is said to be convolved with g (ie f*g)

Question 20

What is the importance of the convolution operation?

Answer 20

it is the basis of digital filtering and image processing
It describes the imaging of an object by the transfer function
An image can be digitally ‘re-imaged’ or manipulated using a mathematical convolution operation

Question 21

What are the dirichlet conditions?

Answer 21

1. f(x) is defined and single values, except possible at a finite number of points (in the range -L to L)
2. f(x) is periodic with period 2L
3. f(x) and f’(x) are piece wise continuous in -L, L

Question 22

What is the relationship between fourier transforms and convolutions?

Answer 22

the fourier transform of a convolution of two functions equals the product of the fourier transforms of those functions
F[f*g] = F[f].F[g] = F[h]
(frequency spectrum of the image equals the frequency spectrum of the object, modulated by the frequency spectrum of the PSF)

Question 23

What is the modulation transfer function?

Answer 23

frequency spectrum of the PSF

presents a frequency interpretation of the convolution/filtering operation

Question 24

What does the fourier transform of a point object look like?

Answer 24

flat frequency spectrum
for good imaging of an object, the frequency spectrum of the transfer function should leave the object function untouched (MTF should be constant)

Question 25

In reality, what does the modulation transfer function tend to and what is the effect of this?

Answer 25

attenuate the high frequencies (removes the sharpness form the image)