Noise reduction in MRI images using partial differential equations

Abstract

MRI machines use superconducting magnets to create an image. However, these
magnets are very expensive. It is possible to use weaker magnets in a low-eld
MRI, but those will result in a lower signal-to-noise ratio, meaning the images
will be polluted.
An image can be smoothed by viewing it as the initial condition of a partial
dierential equation (PDE) and changing it through time integration. The
choice for the PDE determines the way the image changes.
This paper compares four PDE's: a second-order equation originally proposed
by Perona & Malik, a fourth-order equation as proposed by You & Kaveh,
and both aforementioned equations with a delity term added to them. Said
delity term ensures the result does not deviate too far from the original image.
All methods use a diusion coecient specially desiged to preserve edges.
These methods are tested on two versions of the Shepp-Logan phantom, one
having been corrupted with 'salt-and-pepper' noise, and the other one having
been treated with a Gaussian lter, blurring the image.
The salt-and-pepper phantom is improved most by applying the Perona-
Malik method with a delity term. This method gives a good balance between
removing noise and preserving edges and details within the image.
For the blurry phantom the best result is seen using Perona-Malik, where
some of the edges become more dened. However, a delicate balance has to be
kept between rening the edges and blurring out any lower-contrast detail, and
the total eect is limited.
The methods are also tested on images that were created using a prototype
of a low-eld MRI machine. The noise in these images is mostly the 'saltand-
pepper' type. Though the preferred result is somewhat subjective, the
Perona-Malik method with delity once again gives the clearest image here.