Basic principle of Image Formation: ADC convolution Flashcards
What is suitable for digital processing?
An image function must be digitised both spatially and in amplitude
What is a digitiser for?
Sample and quantize analogue video signal
What does the sampling rate determine?
Spatial resolution of digitized image
What does quantization level determine?
Number of gray levels in digitized image
What is the objective of biomedical imaging system?
Make an object or phenomenon within patient’s body visible to observer
What are the parameters that are required to be minimized?
- Artefact
- Contrast
- Blur
- Noise
- Distortion
How can practical system achieve its goal?
Practical imaging system delivers visual information not distorted beyond limit which allows system to achieve its goal
What are measured from physical principle to an image?
- Ultrasound scanner
- Gamma camera
- X-radiograph
- Thermograph
- MR scanner
- ESI
What is ultrasound scanner?
A distribution of acoustic scattering centres
What is Gamma camera?
Uptake of radiopharmaceutical by counting gamma-ray photons
What is X-radiograph?
Linear attenuation of x-ray photons which are getting through object space
What is thermograph?
A distribution of temperature
What is MR scanner?
Magnitude and phase of precessing photons
What is ESI?
Electrical source imaging
Distribution of electric potential or within brain tissue (based on EEG)
What is ESI?
- Epileptic spike
- Reconstructing brain/cardiac electrical activity from electrical potential measured away from brain
- Determines the location of sources of current in body from measurements of voltages
What is EEG inverse problem?
- Make mathematical model of head and electrical source
- Find location of signal that is responsible for measured EEG data
- Invert EEG back to brain space
What are examples of Electrical source imaging?
- Distributed source - electric current encoded by pixel/voxel colour
- Single dipole sources
What happens in early CT imaging devices?
A narrow x-ray beam is scanned across a patient in synchrony with a radiation detector on opposite side of patient
If the beam is monoenergetic or nearly so, what equation is given for the transmission of x-rays through the patient
I = I0e−µx
What does attenuation depend on?
Properties of tissues
What constitutes a CT image
gray-scale display of
attenuation coefficients
How can gray-scale image be produced that represents various structures in parient?
By assigning gray levels to different ranges of attenuation
coefficients,
How are multiple x-ray transmission measurements obtained?
By scanning a pencil-like beam of x-rays and an NaI detector in a straight line on opposite side of patiemt
How are 160 x 180 = 28,000 x-ray transmission measurements accumulated?
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
How can you obtain one projection of an image?
Source and detector move in parallel
Rotate and obtain another projection
Multiple acquisition with different angulation (arc 180 degrees)
What is analog signal?
Continuous curve
What are the 2 operations that convert analog into digital representation?
- Sampling
2. Quantization
Where does sampling occur?
Time domain (spatial)
What does sampling do?
Convert a time-varying voltage signal into discrete-time signal, a sequence of real numbers
What does quantization replace?
Real numbers with approximation from a finite set of discrete values
What is quantization?
Digitization in the signal value (value) = amplitude signal converted into digital
How does ADC work?
Converts the quantities of real world phenomenon into digital language which is used in control systems, data computing, data transmission and information processing
What specifies the sampling frequency?
clock
What are the steps of ADC?
- Sampling of a sine wave using a 3 bit digitizer
2. Obtain sampled signal –> Quantization
How is continuous curve encoded?
using a 16 bit ADC
Step-like function
3 bit ADC
What does 3 bit ADC allow for?
Maximum 111
8 samples to signal all sigals
What is assigned to quantization?
Numerical value
In form of a binary number
What is resolution of ADC?
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)
What is dynamic range of ADC?
the ratio between the minimum and maximum amplitudes a data acquisition system can capture; typically expressed in decibel (dB). 20*log10(Vmin/Vmax)
What does the dyanamic range describe?
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
What is Aperture Error?
Difference between actual value of input signal and flat-topped sample value
What does an error in clock translate into?
Error in values
When does the Quantisation error appear due to?
Finite resolution of ADC
present in all ADC
varies from 0 to ½ of the least significant bit
What is least significant bit?
LSB is the smallest value which can be resolved by an ADC
What is the consequence of passing an analog signal through Quantisation Error?
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
What is the equation of Quantization error?
Sampled Analog signal - Digitized signal
What is 1D sampling thereom?
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)
What is 2D sampling thereom?
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)
