Filter Issues Bill Thomson City Hospital, Birmingham.
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Fourier analysis Represent a function by sums of ‘sin’ and ‘cos’ terms Represent a function by sums of ‘sin’ and ‘cos’ terms easier maths easier maths need to consider frequencies need to consider frequencies
Transcript of Filter Issues Bill Thomson City Hospital, Birmingham.
Filter IssuesFilter IssuesBill Thomson City Hospital, Birmingham
Use 1D profile dataUse 1D profile data
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Fourier analysisFourier analysis
Represent a function by sums Represent a function by sums of ‘sin’ and ‘cos’ termsof ‘sin’ and ‘cos’ terms
easier mathseasier maths
need to consider frequenciesneed to consider frequencies
sines and cosinessines and cosines
A
wavelength
A = size (amplitude)
Wavelength = distance (cm , pixels etc)
frequency = 1 / wavelength (cm-1 , pixels-1)
Amplitude = same
wavelength = 1/2
frequency = double
A
wavelength
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1st harmonic
Count Profile - Fourier fitCount Profile - Fourier fit
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profile data 1 harmonic
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2nd harmonic
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Amplitude - Frequency plotAmplitude - Frequency plot
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profile data
Special case - if a thin line source , get Modulation Transfer Function
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frequency - pixels-1am
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What Happens to Noisy Data?What Happens to Noisy Data?
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profile data 1 harmonic
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profile data 3 harmonics
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Power SpectrumPower Spectrum
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frequency - pixels-1am
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amp . freq
Normally plot (Amplitude)2 against frequency , on log scale
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Maximum Frequency - Maximum Frequency - NyquistNyquist
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Maxfrequency
Wavelength 2 pixels
Max frequency (Nyquist) 0.5 pixels-1
In practice, maximum frequency relates to resolution
Frequency - PixelsFrequency - Pixels-1-1 or cm or cm-1 -1 ??
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Resolution and filter cut-offResolution and filter cut-off
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FWHM = 3 pixels Equivalent cut-off freq = 1/3 = 0.33pixels-1
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Literature , pixel size = FWHM / 3
Butterworth SettingsButterworth Settings
Automatic FilterAutomatic Filter Uses power spectrumUses power spectrum
10% noise means ‘rejects’ 90% of noise10% noise means ‘rejects’ 90% of noise
based on analysis of four images based on analysis of four images
suggest use it for most clinical imagingsuggest use it for most clinical imaging
ARSAC Cardiac StudyARSAC Cardiac Study2-day protocol 2-day protocol
1000 MBq administration of Tc-99m Tetrofosmin1000 MBq administration of Tc-99m Tetrofosmin
Mean administered activity:Mean administered activity:
Stress:Stress: 935 MBq (51 patients)935 MBq (51 patients)
Rest:Rest: 979 MBq (47 patients)979 MBq (47 patients)
Acquisition ProtocolAcquisition Protocol Rotation 1Rotation 1 = = 250 MBq250 MBq Rotation 2 Rotation 2 = 350 MBq= 350 MBq Rotation 3Rotation 3 = = 400 MBq400 MBq
Rotations 2 + 3Rotations 2 + 3 = = 750 MBq750 MBq Rotations 1 + 2 + 3Rotations 1 + 2 + 3 = = 1000 MBq1000 MBq
Can a ‘better’ filter be used for Can a ‘better’ filter be used for 1000MBq?1000MBq?
4x counts of 250MBq4x counts of 250MBq Better statistics , lower noiseBetter statistics , lower noise Expect to use higher cut-offExpect to use higher cut-off Should give ‘better’ quality imagesShould give ‘better’ quality images
250MBq v 1000MBq250MBq v 1000MBq
Show at different Butterworth cut-off Show at different Butterworth cut-off valuesvalues
Use Autoquant+ display of short Axis Use Autoquant+ display of short Axis viewsviews
See when you are sure which is whichSee when you are sure which is which
250MBq v 1000MBq250MBq v 1000MBq
0.20 cycles per pixel0.24 cycles per pixel0.28 cycles per pixel0.32 cycles per pixel0.36 cycles per pixel0.4 cycles per pixel
Can you tell what it is yet?
Resolution and Pixel SizeResolution and Pixel Size
SPECT resolution 15 – 18mmSPECT resolution 15 – 18mm Pixel size should be 5 – 6mmPixel size should be 5 – 6mm Maximum frequency in an object Maximum frequency in an object
is then 0.33 cycles per pixelis then 0.33 cycles per pixel
Resolution issuesResolution issues
Resolution depends onResolution depends ona)a) detector resolutiondetector resolutionb)b) cut-off frequency of filtercut-off frequency of filter
if filter cutoff is low , filter determines resolutionif filter cutoff is low , filter determines resolution
Cardiac Phantom - collimator Cardiac Phantom - collimator effecteffect
High res
GP
40% more counts with GP collimator
