If it is desired to reduce high frequency 2D spatial noise,
a LPF (Low Passs Filter) can be used by selecting a **LPF** choice.
Then prior to the FFT, the fid image is multiplied by
the specified 2D filter.

The **K-space** gaussian filter has a HWHM
(Half Width - Half Maximum) equal to
the radius specified in **Radius** field.
The FWHM (Full Width - Half Maximum) is simply equal to twice the radius.
The values, *g*(*r*), of the gaussian filter are given for one dimension
in Equation 1 for a *radius* = *h* and an image width of *N* pixels.

The for the HWHM radius, **h**, is
given in Equation 2.

Multiplication in **K-space** is equivalent to convolution in
**Image-space**.

Thus the relationship between gaussian filter FWHM in **K-space** to the
FWHM in **Image-space** can be determined by taking the Fourier
Transform (FT) of the **K-space** gaussian.

But a gaussian with in the numerator is just another gaussian with in the denominator.

By equating the exponents and replacing , the **Image-space**
can be determined.

From equation 2 the **Image-space** HWHM, , is

Substituting for and noting that *FWHM* = 2*h*

Wed Jan 29 11:44:13 CST 1997