Basic principle of Image Formation: ADC convolution

Question 1

What is suitable for digital processing?

Answer 1

An image function must be digitised both spatially and in amplitude

Question 2

What is a digitiser for?

Answer 2

Sample and quantize analogue video signal

Question 3

What does the sampling rate determine?

Answer 3

Spatial resolution of digitized image

Question 4

What does quantization level determine?

Answer 4

Number of gray levels in digitized image

Question 5

What is the objective of biomedical imaging system?

Answer 5

Make an object or phenomenon within patient’s body visible to observer

Question 6

What are the parameters that are required to be minimized?

Answer 6

1. Artefact
2. Contrast
3. Blur
4. Noise
5. Distortion

Question 7

How can practical system achieve its goal?

Answer 7

Practical imaging system delivers visual information not distorted beyond limit which allows system to achieve its goal

Question 8

What are measured from physical principle to an image?

Answer 8

1. Ultrasound scanner
2. Gamma camera
3. X-radiograph
4. Thermograph
5. MR scanner
6. ESI

Question 9

What is ultrasound scanner?

Answer 9

A distribution of acoustic scattering centres

Question 10

What is Gamma camera?

Answer 10

Uptake of radiopharmaceutical by counting gamma-ray photons

Question 11

What is X-radiograph?

Answer 11

Linear attenuation of x-ray photons which are getting through object space

Question 12

What is thermograph?

Answer 12

A distribution of temperature

Question 13

What is MR scanner?

Answer 13

Magnitude and phase of precessing photons

Question 14

What is ESI?

Answer 14

Electrical source imaging

Distribution of electric potential or within brain tissue (based on EEG)

Question 15

What is ESI?

Answer 15

1. Epileptic spike
2. Reconstructing brain/cardiac electrical activity from electrical potential measured away from brain
3. Determines the location of sources of current in body from measurements of voltages

Question 16

What is EEG inverse problem?

Answer 16

1. Make mathematical model of head and electrical source
2. Find location of signal that is responsible for measured EEG data
3. Invert EEG back to brain space

Question 17

What are examples of Electrical source imaging?

Answer 17

1. Distributed source - electric current encoded by pixel/voxel colour
2. Single dipole sources

Question 18

What happens in early CT imaging devices?

Answer 18

A narrow x-ray beam is scanned across a patient in synchrony with a radiation detector on opposite side of patient

Question 19

If the beam is monoenergetic or nearly so, what equation is given for the transmission of x-rays through the patient

Answer 19

I = I0e−µx

Question 20

What does attenuation depend on?

Answer 20

Properties of tissues

Question 21

What constitutes a CT image

Answer 21

gray-scale display of

attenuation coefficients

Question 22

How can gray-scale image be produced that represents various structures in parient?

Answer 22

By assigning gray levels to different ranges of attenuation

coefficients,

Question 23

How are multiple x-ray transmission measurements obtained?

Answer 23

By scanning a pencil-like beam of x-rays and an NaI detector in a straight line on opposite side of patiemt

Question 24

How are 160 x 180 = 28,000 x-ray transmission measurements accumulated?

Answer 24

the angular orientation of the scanning device is incremented
1 degree, and a second translational scan of 160 transmission measurements is performed. This process of translational scanning separated by 1-degree increments is
repeated through an arc of 180 degrees

Question 25

How can you obtain one projection of an image?

Answer 25

Source and detector move in parallel
Rotate and obtain another projection
Multiple acquisition with different angulation (arc 180 degrees)

Question 26

What is analog signal?

Answer 26

Continuous curve

Question 27

What are the 2 operations that convert analog into digital representation?

Answer 27

1. Sampling

2. Quantization

Question 28

Where does sampling occur?

Answer 28

Time domain (spatial)

Question 29

What does sampling do?

Answer 29

Convert a time-varying voltage signal into discrete-time signal, a sequence of real numbers

Question 30

What does quantization replace?

Answer 30

Real numbers with approximation from a finite set of discrete values

Question 31

What is quantization?

Answer 31

Digitization in the signal value (value) = amplitude signal converted into digital

Question 32

How does ADC work?

Answer 32

Converts the quantities of real world phenomenon into digital language which is used in control systems, data computing, data transmission and information processing

Question 33

What specifies the sampling frequency?

Answer 33

clock

Question 34

What are the steps of ADC?

Answer 34

1. Sampling of a sine wave using a 3 bit digitizer

2. Obtain sampled signal –> Quantization

Question 35

How is continuous curve encoded?

Answer 35

using a 16 bit ADC

Question 36

Step-like function

Answer 36

3 bit ADC

Question 37

What does 3 bit ADC allow for?

Answer 37

Maximum 111

8 samples to signal all sigals

Question 38

What is assigned to quantization?

Answer 38

Numerical value

In form of a binary number

Question 39

What is resolution of ADC?

Answer 39

is the number of discrete values it can produce over the range of analog values. Measured in bits

8 bit – max 256 levels (28)
16 bit – max 65536 levels (216)
24 bit – max 16777216 levels (224)

Question 40

What is dynamic range of ADC?

Answer 40

the ratio between the minimum and maximum amplitudes a data acquisition system can capture; typically expressed in decibel (dB). 20*log10(Vmin/Vmax)

Question 41

What does the dyanamic range describe?

Answer 41

the range of the input signal levels that can be reliably measured simultaneously, in particular the ability to accurately measure small signals in the presence of the large signals

Question 42

What is Aperture Error?

Answer 42

Difference between actual value of input signal and flat-topped sample value

Question 43

What does an error in clock translate into?

Answer 43

Error in values

Question 44

When does the Quantisation error appear due to?

Answer 44

Finite resolution of ADC
present in all ADC
varies from 0 to ½ of the least significant bit

Question 45

What is least significant bit?

Answer 45

LSB is the smallest value which can be resolved by an ADC

Question 46

What is the consequence of passing an analog signal through Quantisation Error?

Answer 46

8 bit digitizer adds noise of up to 1/512 of the full scale value;
12 bit conversion adds a noise of up to 1/8192 of the full scale;
16 bit conversion adds 1/131072

Question 47

What is the equation of Quantization error?

Answer 47

Sampled Analog signal - Digitized signal

Question 48

What is 1D sampling thereom?

Answer 48

A continuous-time signal x (t), whose spectral content is limited to frequencies smaller than Fb (i.e., it is band-limited to Fb) can be recovered from its sampled version x (n) if the sampling rate is larger than twice the bandwidth (i.e., if Fs > 2Fb)

Question 49

What is 2D sampling thereom?

Answer 49

A continuous-space signal s (x; y), whose spectral content is limited to spatial frequencies belonging to the rectangle having semi-edges Fbx and Fby (i.e., band limited to Fbx and Fby) can be recovered from its sampled version s (m; n) if the spatial sampling rates are larger than twice the respective bandwidths (i.e., if Fx > 2Fbx and Fy > 2Fby)