Instrumentation and Computers in Imaging Flashcards
What is the difference between analogue and digital?
Analogue= continuous (parameters are infinitely variable) Digital = discrete
What is binary?
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).
How does an ADC affect data?
Analogue digital converter = loses data
Sensor: mA -> mV
Why doesn’t a transducer produce a perfect signal?
Errors / artefacts Transfer function Properties • Noise • Saturation • Linearity • Dynamic range • Resolution
What is the differnce between a perfect and a truthful transducer signal output?
draw graph
- straight line =perfect
- wiggled = truthful
What is the process of digital acquisition?
- 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
Why does discretisation damage data?
• 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
Why is 44kHz data stream chosen for audio CD?
Human hearing = 20kHz,
Satisfies nyquist sampling rate (2x frequency)
How does MRI system work?
o Produces proton density map
o Analogue - RF emissions
o Digitise RF amplitude and phase (ADC)
How does Digital X Ray system work?
o Maps X-ray intensity
o Analogue detector is film/CCD
o Digitisation by ADC -> computer
What is the series of events for digital imaging?
- continuous quantity
- sensor (transducer - convert to mA/mV)
- ADC (calibration)
- Number (integer in computer)
- Process
- Displace
Why does an image not faithfully represent the object?
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
What is a point spread function?
smeared representation of the point
What is the transfer function?
function that transforms the object to the image
When is the transfer function and the point spread function the same?
for an object consisting of a single point
What is the amplitude of point spread function modulated by?
amplitude of the object point
Where is the point spread function centred?
on the object point
On multipoint images, how is the point spread function calculated?
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
What is the convolution integral?
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)
What is the importance of the convolution operation?
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
What are the dirichlet conditions?
- f(x) is defined and single values, except possible at a finite number of points (in the range -L to L)
- f(x) is periodic with period 2L
- f(x) and f’(x) are piece wise continuous in -L, L
What is the relationship between fourier transforms and convolutions?
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)
What is the modulation transfer function?
frequency spectrum of the PSF
presents a frequency interpretation of the convolution/filtering operation
What does the fourier transform of a point object look like?
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)
