Filter Issues Bill Thomson City Hospital, Birmingham

Use 1D profile data profile

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

sines 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

Count Profile - Fourier fit

Amplitude - Frequency plot Special case - if a thin line source, get Modulation Transfer Function

What Happens to Noisy Data?

Power Spectrum Normally plot (Amplitude) 2 against frequency, on log scale

Maximum Frequency - Nyquist pixels Max frequency Wavelength 2 pixels Max frequency (Nyquist) 0.5 pixels In practice, maximum frequency relates to resolution

Frequency - Pixels -1 or cm -1 ?

Resolution and filter cut-off FWHM = 3 pixelsEquivalent cut-off freq = 1/3 = 0.33pixels -1 Literature, pixel size = FWHM / 3

Butterworth Settings

Automatic Filter Uses power spectrum Uses power spectrum 10% noise means ‘rejects’ 90% of noise 10% noise means ‘rejects’ 90% of noise based on analysis of four images based on analysis of four images suggest use it for most clinical imaging suggest use it for most clinical imaging

ARSAC Cardiac Study 2-day protocol 1000 MBq administration of Tc-99m Tetrofosmin Mean administered activity: Stress:935 MBq (51 patients) Rest:979 MBq (47 patients)

Acquisition Protocol Rotation 1 = 250 MBq Rotation 1 = 250 MBq Rotation 2 = 350 MBq Rotation 2 = 350 MBq Rotation 3 = 400 MBq Rotation 3 = 400 MBq Rotations = 750 MBq Rotations = 750 MBq Rotations = 1000 MBq Rotations = 1000 MBq

Can a ‘better’ filter be used for 1000MBq? 4x counts of 250MBq 4x counts of 250MBq Better statistics, lower noise Better statistics, lower noise Expect to use higher cut-off Expect to use higher cut-off Should give ‘better’ quality images Should give ‘better’ quality images

250MBq v 1000MBq Show at different Butterworth cut-off values Show at different Butterworth cut-off values Use Autoquant+ display of short Axis views Use Autoquant+ display of short Axis views See when you are sure which is which See when you are sure which is which

250MBq 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 Size SPECT resolution 15 – 18mm SPECT resolution 15 – 18mm Pixel size should be 5 – 6mm Pixel size should be 5 – 6mm Maximum frequency in an object is then 0.33 cycles per pixel Maximum frequency in an object is then 0.33 cycles per pixel

Resolution issues Resolution depends on Resolution depends on a)detector resolution b)cut-off frequency of filter if filter cutoff is low, filter determines resolution if filter cutoff is low, filter determines resolution

Cardiac Phantom - collimator effect High res GP 40% more counts with GP collimator