How Do We Set Filter Parameters

The cut-off frequency is probably the most important parameter in filtering work.

 

The cut-off frequency is chosen based on:

·         The object being imaged.

·         Count density in the image

·         Camera system and it's spatial resolution.

·         Pixel size.

 

Overall,  the cut-off frequency should be chosed based on the frequency space distribution of the data (i.e. the power spectrum of the object being imaged) and the associated noise level in the images.

 

 

Count Density Issues And Associated Noise Levels.

 

Note that the noise level in our images will depend on the count density of the image.

 

The higher the count density in our images the lower the noise level in relation to the image's power spectrum (i.e. the higher the frequency at which the two meet or interesect in the power spectrum).

 

 

 

High Count Density Image Power Spectrum:


 

 

 


Low Count Density Image Power Spectrum:


 

 

 


Camera system and it's spatial resolution effects.

 

The natural resolution of the camera and associated pixels will also affect the way we chose the cut-off frequency of our filters.

 

According to discrete sampling theory, the maximum usable frequency is 0.5 cycles per pixel because at least two pixels are required to define the one cycle of the wave.

 

This frequency is called the "Nyquist Frequency" (0.5 cycles/pixel).

 

If the Nyquest frequency  is given in cycles/cm then it will vary for different pixel sizes.

 

When filtering, the cut-off frequency is ALWAYS chosen to be less than the Nyquist Frequency.

 

·         If the cut-off frequency is chosen higher than this then frequencies greater than 0.5 cycles/cm will be included in the image and will cause Aliasing artifacts.

 

 

Summary of Cut-off Frequency Decisions

 

          1.       One criteria is to set the cut-off frequency to a value approximately equal to the or the Nyquist frequency which is related to the resolution of the camera ( ~ 1 cm or so depending on your camera).

à                  This is because nuclear medicine cameras cannot resolve images smaller than a certain size.

à                  Again, this is related to the Nyquist Frequency of our camera system.

 

          2.       The second criteria could be to set the cut-off frequency (or to match the point of the filter where it drops to zero) to the value where the images “power-spectrum” and noise level meet.

 


 

 


Order or Roll-off of the Filter

 

          à      How quickly the transition is made between frequencies that are kept and frequencies that are eliminated.

 

          à      It is difficult to see the influence of changing the order of a filter while maintaining a constant cut-off frequency.

 

          à      The only real “rule or thumb” is that if the order is set too high, then oscillations in the image intensity will be introduced.

 

 

 How Do We Chose Which Type Of Filter To Use?

 

There is no perfect filter!!!!

 

So, the "best" filter for you to use depends on:

 

Basic principles to think about when choosing a filter for a given task:

1.     All images reconstructed with backprojection require filtering with a ramp filter.

2.     A cutoff window is required to remove the image noise that was enhanced by the ramp filter.

3.     A smooth cut-off is required to prevent the creation of "rippling" artifacts.

4.     The cut-off frequency should never be higher than the Nyquist Frequency (0.5 cycles/pixel).

5.     The choice of cut-off frequency is a compramise between smoothness of the image and spatial resolution.

6.     Images with higher count densities should use higher cut-off frequencies.

 

 

When trying to decide on an appropriate filter for a given protocol here are some helpful tips:

 

1.     Begin with the filter and parameters suggested by the manufacturer.

2.     Try filters suggested by respected collegues that use the same camera, computer and protocols.

3.     Try filter values given in the literature.

4.     Try changing the filter parameters on your system and carefully dtermine the effects of the changes on the resultant clinical image (especially on the clinical interpretation of these images). 

·         Do Not be afraid to try new filtering parameters.  However, the final decisions will be made by the physicians that read the scans.

5.     Perform phantom studies that closely approximate the organs of interest and optimize the filter parameters for different clinical situations (i.e. different image count densities).

6.     When doing studies which will be compared to a normal database make sure that you use the same filtering parameters as the normal data.

 

 

Cautions when working with filters:

1.     Remember that the units of cut-off frequency are not consistent between vendors.

·         Cycles/cm 

·         Cycles/pixel

·         Fraction of Nyquist Frequency (0.5 cycles/pixel)

·         Harmonic Number

 

              Note:          Cycles/cm is thought to be the best one b/c it's independent of camera size and pixel matrix size.

 

2.     Not all filter shapes are defined consistently between vendors and could have different meanings for the cut-off frequencies.

·         The butterworth filter is a prime example.