Biomedical Engineering Reference
In-Depth Information
The SNR values for the images in Figure 7.1 from left to right are 0:8378
(Original), 0:8951 (Mean), 0:8514 (Median), and 0:8536 (Wiener), respectively.
These example values show that all filtered images have a higher SNR than
the original image, indicating a reduced noise level. Obviously, the lower the
variance of the image is the higher the SNR gets.
The peak SNR is a further common variant of the SNR. It measures the
relation between the maximum intensity of an image and its noise component.
Definition 15 (PSNR) Let L define
the
maximum
intensity
of
a
non-
constant image I. The peak signal to noise ratio (PSNR) is defined as
L
(I)
L
PSNR(I) := 20
log
10
= 20
log
10
q
1
jj
; (7.39)
·
·
R
(I(x) (I))
2
dx
where is the expected value and the standard deviation.
SNR and PSNR have in common that the denominator is the standard devi-
ation. They differ in the numerator which is the expected value for SNR and
the maximum intensity for PSNR. The logarithmic scaling in the definition of
PSNR is used to express the noise ratio in decibels.
7.7.2 Phantoms
The validation of many image processing techniques is done using phan-
toms as they provide complete knowledge about anatomy and/or physiology
and therefore ground-truth information. This is an advantage compared to
real data which generally lacks ground-truth information.
Phantoms can be subdivided into hardware and software phantoms. Hard-
ware phantoms are commonly used to validate scanner geometry or recon-
struction software. Software phantoms, however, can be used for validation
of image processing tasks. These two kinds of phantoms are discussed in the
following.
7.7.2.1
Hardware
Hardware phantoms can be used for validating scanner geometry, attenua-
tion and scatter correction or alignment tasks in multimodal imaging. Further,
hardware phantoms are the established way to determine the scanner resolu-
tion. They are inevitable for quantitative measurements.
Most hardware phantoms available for emission tomography are commer-
cial like Jaszczak or NEMA [2, 8, 14] phantoms. The commercially available
hardware phantoms cover simple geometry phantoms or more detailed brain,
cardiac, or lung phantoms. Phantoms applicable to multimodal imaging tech-
niques like SPECT/CT or PET/CT are also available. Especially for combined
approaches, where the coordinate systems of the different scanners need to be
calibrated, phantoms are essential.
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