Contrast, Image Noise, Quantum
Mottle
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All
imaging techniques depend on differential emission of energy from the imaged object
according to some physical property of the object. Without differential emission,
the measured signal would contain no information about the imaged object and
the only variations would be informationless noise. Contrast is a measure of
the magnitude of the measured signal differences between physically different
regions of the imaged object. When these measured signals are converted into an
image ‘contrast’ describes the magnitude of intensity differences between
different regions in the image. We can thus think of image contrast as being
the product of signal contrast and detector contrast:
CI = D CS x CD
The
signal contrast (CS) depends on the energy source and the physical properties
of the imaged object – it describes the range of energies emitted by the
object. The detector contrast (CD) depends on the way the signal emitted by the
imaged object is modified (e.g. with a scatter suppression grid), detected, and
recorded. We need both signal and detector contrast to form image contrast.
The
signal contrast (CS) depends on the energy source and the physical properties
of the imaged object – it describes the range of energies emitted by the
object. The detector contrast (CD) depends on the way the signal emitted by the
imaged object is modified (e.g. with a scatter suppression grid), detected, and
recorded. We need both signal and detector contrast to form image contrast.
Image Noise
No
imaging method works without contrast and no imaging method is free of noise.
If contrast is low and noise is high then the random intensity variations due
to noise will make it difficult to visually detect the intensity changes due to
contrast. How an increasing level of noise relative to contrast diminishes our
ability to distinguish objects in an image. But before discussing the
interrelation between noise and contrast we will first consider the origin and
types of noise found in medical images.
What Is Noise?
The
everyday answer to this question is ‘Annoying sounds that make it difficult to
hear what you want to hear’. In terms of imaging, a similarly broad definition
would be ‘Any intensity or colour fluctuations that make it difficult to see
what you want to see’. The problem with these definitions is that we often
don’t know what it is we are supposed to be hearing or seeing – some or even
all the information is hidden by the noise. What we want ideally is to be
confident about the information we receive. If you were on a very noisy phone
connection you might ask your caller to repeat a sentence three times before
you are sure you know all the words in the sentence. You may never hear one
sentence fully due to the noise but so long as the caller repeats the same
sentence each time you eventually know what all the words are. When we make an image,
we can effectively do the same thing to reduce the uncertainties due to noise –
we either measure the signal for a longer time or repeat the measurement
several times, which is effectively the same. If the noise is random its
contribution to the total image signal will diminish over time or repeated
measurements.
What
happens if the noise is not random? This type of noise does not decrease when
the measured signal is averaged over time. It can appear due to leakage of a
spurious signal into the system (from the mains power supply for example), or
some systematic ‘error’ in the method of formation of the image. The latter
type of signal is generally referred to as an artefact.
Focusing
on imaging we can, at least conceptually, separate the energy we measure, the
image (I), into ‘true’ signal variations that are characteristic of the imaged
object (S), and ‘spurious’ or ‘random’ variations that are not characteristic
of the imaged object – in other words, noise (N) (and possibly artefacts but we
will ignore these for now):
I = S + N
While
we would generally think of the ‘signal’, S, as always being positive, the
noise, N, could be expected to make either positive, zero, or negative
contributions to measurement. The ‘erroneous’ measurement value it causes may
be either higher or lower than the ‘true’ signal measurement expected. In many
cases, we can say that the average (mean) measurement error due to noise is
zero. This is ‘zero-mean’ noise.
In
general, we have no way of separating ‘true signal’ from ‘random noise’. Nevertheless,
the concept of separable signal and noise is very useful in signal and image
processing. This does, however, cause some potentially confusing terminology.
When we talk about the intensity of the energy we measure or ‘detect’ this is
usually referred to as ‘the signal’ – ‘I’m not getting a signal!’ or ‘The
signal is strong enough, but it’s very noisy’. A few seconds later somebody
will ask, ‘What’s the signal-to-noise ratio?’ Suddenly the meaning of ‘signal’
has changed. In discussions that include noise, ‘signal’ usually means the
notional ‘true’ signal, free of noise, coming from the object of interest. If
the discussion does not explicitly mention noise then ‘signal’ probably means
the intensity of detected energy, including noise. Most of the time the context
is sufficient to work out which usage is applicable.
Quantum Mottle
Going
back to our general definition of image noise as ‘Any intensity or colour fluctuations
that make it difficult to see what you want to see’ we should include random
fluctuations in the flow and spatial distribution of energy from the energy
source itself. In the majority of medical imaging methods, the energy source
directly (or, in the case of PET, indirectly) emits electromagnetic radiation
or photons. The particulate nature of electromagnetic radiation has a profound
effect on the nature of noise in these medical images. The probability of a
photon being detected in any region of the image sensor during any specific
interval of time is constant. We can see this effect if we look closely at the
background of a radiograph where the variation in measured intensity is due
entirely to the (locally) random distribution of photons emitted by the X-ray
source. This random ‘texture’ is called Quantum mottle.