Noise reduction in MRI images using partial differential equations
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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.